After the production of the Marder III had phased out in the summer of 1944, the new Hetzer was also referred to as Panzerjäger 38 t or “38(t)”, even though the official designation was Jagdpanzer 38 (with or without “t”). The same happened with the first version of the Jagdpanzer IV (Ausf. F, which was based on a shortened Panzer IV chassis, with the Pak 39).

In order to avoid confusing the Hetzer with the Marder, the Hetzer’s Pak 39 L/48 gun was often included in the designation, when using the designation “Panzerjäger” for the Hetzer in official documents, (hence “Panzerjäger 38 t mit Pak 39″) as can be seen in the Hetzer’s field manual.

The same goes for the Jagdpanzer IV with the Pak 39. While in general the germans had used vehicles designations or names rather consistently, some tanks received a somewhat confusing and less consistent treatment.

Also, in reality, the Jagdpanzer IV with Pak 39 (also designated “Jagdpanzer IV/48″) had 60mm frontal armor and 30mm of upper and lower side armor. It could carry 79 rounds. Around 769 vehicles were produced. Officially, this design was rejected either by Hitler or Army Ordnance, but after Panzer IV chassis had been taken out of the production line and shortened for the TD production, the production went and issuance to troops went on until halted in 1944. Some sources indicate that +/- 769 vehicles had been produced.

But the most produced version (more than 1200 vehicles, over 900 of them were VOMAG versions) was in fact the Jagdpanzer IV/70, though, which was produced by two different companies and had resulted in 2 differing designs, where then the first design by ALKETT (~300 tanks produced) was used as a stop-gap tall version that would allow for mounting a slightly modified Panther gun immediately, until the company VOMAG could free resources to modify and produce the lower silhouette version they had designed. Both versions, the Jagdpanzer IV/70(A) and the Jagdpanzer IV/70(VO) used a minimally modified variant of the Panther gun, now designated StuK 42/L70, and their frontal glacis featured 80mm of armor, while their lower sides had 30mm armor, but their upper sides 40mm of armor (30°), instead of 30mm on the Pak 39 version, now.
The IV/70 could carry 55 rounds.

That said, the Jagdpanzer IV with its different guns in WOT is a mash-up of 3 different historical versions produced by the Germans.

Initially, the official designation was “Panzerjäger 38(t) für 7,62 cm PaK 36(r)” and was then changed to the shorter “Panzerjäger 38(t)”. But even official German documents would sometimes refer to it as “Panzerjäger 38″, without the “(t)” indicating its czech (“t” for “tschechisch”) origin, or “Panzerjäger 38 t”.

Some German military historians indicate that the 75mm-Pak 40 Marder “H” version could carry 38 rounds.

Some of these sources also state that the engine was not moved to the middle but to the front for the “M” version of the Marder.
Whatsoever, the M version was not only the most produced version, it had also the most/best streamlined design, like the turret (which still could be traversed 21 degrees to each side) that now blended in with the turret side armor, which was actually fixed now.
http://ww2db.com/images/vehicle_marderiii_2.jpg

Scans of the original field manual for the Hetzer (24.6.44), approved and issued by Guderian, show that the Germans referred to the Hetzer as “Panzerjäger 38 t”.
Original text: “Bedienungs- und Schießanleitung für die le. Panzerjäger IV und 38 t mit der Pak 39.”

The “(t)” was indeed used for such tanks in some of the sheets documenting the required strengths for every unit (short known as “KStN”) and other documents, but (eg.) just the designation and a “t” behind it was also used quite often, as you can see in the Panzerjäger manual. Other agencies/officials used the designations Jagdpanzer 38(t), Jagdpanzer 38 t, or just Jagdpanzer 38.
It was the same with the Panzerjäger 38 Marder III.

The scans of the field manual for JgPz IV and 38 t:
http://www.lexikon-der-wehrmacht.de/Waffen/Merkblatt/Hetzer.htm

For the Marder “III”, captured Russian 76.2mm field guns (!) and AT guns (designated “7.62-cm-PaK 36 (r)”, velocity : 740 meters/sec. – with regular AP rounds able to pen. 82mm of armor at an angle of 60 degrees and a range of 1000 meters, 990 meters/second with tungsten core rounds – able to pen. 112mm at 1000 meters) were then mounted on the Panzerkampfwagen 38 (t) chassis. The official designation: “Panzerjäger 38″ or “Sd. Kfz 139″. The loading chamber was modified so that the 76.2mm AT guns could fire captured Russian rounds OR the 75mm rounds also used by the German 75mm-PaK 40 and German tanks. With the regular German 75mm AP round, the gun could penetrate 94mm of armor at a range of 1000 meters (60 degrees). This version of the Marder III could carry 30 rounds.

On 27th of February 1944, Hitler ordered to add and use the nickname “Marder III”, so it was then designated Panzerjäger 38 “Marder III”, officially.

The armor around the gun mount (protecting gunner and loader) was 14.5mm on the front and only 10mm on the side. This meant that both gunner and loader were protected from rifle or machine gun AP rounds (called “SmK” bullets in the German military, 7.62mm) fired at the front/sides, but Russian AT-rifle rounds (14.5mm) could pierce through easily, already.
Around 344 Marder III had been produced until the end of October 1942, where 176 of these tanks were based on the Ausführung G model of the PzKpfw 38 (t). Another batch of 19 Marder III based on the Ausführung “G” was produced by converting Panzerkampfwagen 38 (t) tanks that were in need of repair (and pulled back from the front) to the Marder G standard in 1943.
The “G” version had a top speed of 42 km/h, the gun could be traversed 21 degrees to each side (42 degrees field of vision), but the turret could be turned as well (not sure by how much, but the additional traverse was notable, as the gun/”turret” was mounted on a traverse pod)

In November 1942, the production was shifted to equip the Marder III with the “75mm-PaK 40″, a very capable German AT-gun, and the Marder platform was now built based on the Ausführung “H” models of the Panzerkampfwagen 38 (t).
Even though the order for the PaK 40′s development was issued as early as 1938, as the Army ordnance office had figured in 1938 already that the 50mm-PaK 38 would not be able to deal with well armored French tanks of the time, the first 15 guns started to be issued to Army infantry units as late as February 1942, at a point where infantry units were in desperate need of capable AT guns, due to the appearance of the T-34 on the Eastern front.

One reason for shifting to the 75mm-PaK 40 on the Marder III as late as November 1942 may have been the possibility, that – at the time of development of the Marder III – the 75mm-Pak 40 was either still in development or its delivery priority set to infantry AT units, so that only after the production had reached sufficient output numbers after summer 1942, the Marder III could be equipped with the gun as well.
The Pak 40 delivered a velocity of 770 meters/second with regular AP rounds (Panzergranate 39) and 990 meters/second with tungsten rounds, which eenabled it to penetrate 94 mm of armor using regular AP rounds at an angle of 60 degrees and a range of 1000 meters and 96 mm of armor at the same distance with tungsten/hard core round. Even though it might look like the russian AT gun had more punch than the PaK when using tungsten rounds, the German PaK showed way better results with regular AP rounds. Also, the Germans suffered of a lack of tungsten, so that they halted production and issuance of tungsten rounds around 1942/early 1943. Since a number of tungsten rounds were still floating around, German tanks would carry 1 or 2 tungsten rounds for “emergency” situations where regular rounds would not penetrate or not inflict succicient damage.

A skilled infantry AT crew (5 men) could fire 15 rounds per minute with the Pak 40.

The first prototype of the Marder III with the 75mm-Pak 40 finished in June 1942 had undergone modifications in order gain room for the new gun (redesigned baseplate section) and it also featured an improved “turret”/gun shield, where some batches of the serial production version had also received additional armor plates resembling a turret roof to improve crew protection, while the back was still open. As with previous versions, when firing, the only crew member being protected by the chassis (glacis) armor was the driver.

The max. speed of the “H” model Marder III was now 47 km/h. The production of the Marder III based on Ausf. H phased out in Mai 1943 after 242 vehicles. Another batch of 175 vehicles was converted in 1943 by using damaged Panzerkampfwagen 38 (t) that were sent back for repairs.
From March 1942 – May 1943, 761 Panzerjäger 38 (t) were produced.

In May 1943 production based on PzKpfw 38(t) Ausf. M started, where some may have been equipped with a remaining number of stocked PaK 40.

Since the improved 75mm-PaK 40/3 became available around the same time, it could now be mounted on M models, so it seems like all following vehicles had received the new PaK gun.
In order to be able to fit the gun, the engine and gear had to be moved from the rear to the front part of the tank, which then allowed for mounting the gun (with its turret) on the rear end of the tank. This allowed for faster reloading and easier access to the gun compartment, but also for a way lower silhouette. The armor of the turret/gun structure was now 10mm on all sides (front and side, and also roof if present). These vehicles were designated/considered to be Marder III as well, they just received the number Sd. Kfz. 138, to indicate that it was the Marder III with Pak 40/3 and changed turret position.
Due to those changes this version of the Marder III could hold 27 rounds, only.
975 of the Marder III with the 75mm-Pak 40/3 were produced until Mai 1944, when production of the Marder III phased out finally.

Due to the production numbers, the Marder III with Pak 40/3 at the rear can be considered the main production version, and not the Marder III depicted in WOT.
Also, it’s a pity that the turret of the Marder can’t be traversed in the game, whereas in reality it offered an extended field of view/gun traverse, adding to the 42 degrees simply offered by the gun (mount).