The numbers that follow the index could mean a number of things. They could mean the caliber (SU-152), tank of origin (SU-26), or be a sequential index (SU-5). This article will go through the SU indexed vehicles, and give a brief description of them.
SU-1
The SU-1 was developed way back in 1931 on the T-26 chassis. A 76.2 mm short barreled model 1927 gun was located in a casemate. Gun depression was -5 degrees, elevation was 23 degrees 30 minutes, and horizontal aiming was 5 degrees each way. The vehicle also had two DT machine guns. It had armour up to 13 mm thick, and could achieve a speed of up to 30 kph. Tested in December of 1931, it did not pass trials. An improved version based on the T-26-4 was developed, but never built.
SU-2
The index SU-2 was given to a more artillery-like vehicle, a 76.2 mm model 1902 gun on the back of a Kommunar 9GU tractor. The gun could rotate 360 degrees. The vehicle had 10 mm of armour all around. It could reach a maximum speed of 12 kph, and did not pass trials. Read about other Soviet tractor tank projects here.
SU-3
Going back to a tank-like vehicle, the SU-3 (also called SU-76K, or T-27K) was based on the T-27 tankette. It was created in 1933 to accompany scout groups and cavalry, which explains its relatively high speed compared to the previous SUs (45 kph). The gun was a recoilless 76.2 mm "K" Kurchevskiy semi-automatic gun, installed instead of the regular machine gun. Its traverse was quite small: 5 degrees to the side, 1 down, 5 up. Armour was up to 9 mm.
SU-4
The SU-4 was vastly different from previous vehicles. While using the same Kurchevskiy 76.2 mm recoilless gun, it was mounted on a GAZ-A truck, instead of a tracked vehicle. Unlike with the SU-3's limited traverse, the gun could rotate 360 degrees. The armour was not thick: the 6 mm gun shield was the only armoured component of the vehicle. Thanks to this, the SU-4 could reach a 63.2 kph top speed. 23 of these vehicles were built from 1934 to 1937. Colonel-general Arhipov recalls them favourably in his book "Time of Tank Attacks". He doesn't call them by name, referring to them as "recoilless guns on a rotating mount on the back of a truck", but their effectiveness in battle was unambiguous: "The howitzer division and recoilless guns worked very effectively. The shell from such a gun could effortlessly penetrate the front armour of German medium tanks, not to mention the light PzI and PzII."
SU-5
The in-game SU-5 isn't actually called SU-5. The vehicle in game could be either a SU-5-2 or SU-5-3, depending on the gun you put on it. The first vehicle to earn the SU-5 designation was another Kommunar 9GU based vehicle, this time with no armour at all, and a 76.2 mm model 1915 AA gun. A prototype was manufactured and built in 1932, but scrapped due to the Kommunar 9GU chassis being too weak for a 76.2 mm gun.
SU-6
The SU-6 was built in 1934, again on a T-26 chassis. A prototype was built in 1935. In 1937, four more SU-6es were built. The hull of a SU-6 was wider and longer than a T-26, with an extra road wheel and folding 8 mm thick armoured sides to protect the crew during transit. The SPG was armed with a model 1931 76.2 mm 3K AA gun. The gun could rotate fully, elevate to 82 degrees, and depress to -5 degrees. The rate of fire was 20 RPM. During trials, it was also equipped with a 37 mm AA autocannon.
SU-7
The SU-7 was a heavy SPG with a 203 mm B-4 or 305 mm Br-18 howitzers, based on a special chassis developed at factory #185, based on the T-35. Gun elevation was up to 52 degrees with the B-4, or 70 degrees with the Br-18. The gun had a horizontal traverse of 84 degrees. The project also called for a 400 mm mortar, but it was dropped from the later versions of the design. Elements of the SPG were built, but scrapped when all heavy SPG projects were cancelled in 1937.
SU-8
You should all know the SU-8 from the Soviet artillery tree (where, at least until the next patch, it occupies a spot at tier 5). However, it differs somewhat from the historical SU-8. The SU-8 started development in 1934, as a mobile AA gun. For this task, it was armed with a 76.2 mm 3K AA gun. Like with the SU-6, it could rotate fully. The armour ranged from 8-20 mm, with 15 mm folding screens to protect the crew. Two variants of the SPG existed: one with a front mounted gun, and one with a rear mounted gun. Although, technically, both guns were located in front of the T-28 chassis. In the case of the "rear" gun (the one in game), the chassis was reversed. The speed of the front gun SU-8 was 40 kph, and the speed of the rear gun SU-8 was 48 kph.
SU-10
SU-10 (or SU-BU-10) was a coastal gun project developed in 1933. The vehicle consisted of a 152.4 mm B-10 naval gun on a T-28 chassis, with a curious feature: when deployed, the SPG could rotate 360 degrees using a special deployable mount. In this mode, the engine power would rotate the SPG instead of moving the tracks. The armour of this vehicle was between 8 and 20 mm, and its projected speed was 20 kph.
SU-12
SU-12 was another truck project. In 1933, 76.2 mm model 1927 guns were mounted on Morland and GAZ-AAA trucks in a fully rotating turret. Despite the turret technically being able to rotate fully, firing with the gun forward was a bad idea, as the gases exiting the barrel would bend the roof. The safe range of fire was 270 degrees. Unlike with the SU-4, the crew was protected from four sides by 4 mm thick shields, instead of just one. After successful trials in 1933, 99 vehicles were produced. These vehicles fought at Khalkin-Gol, Lake Hasan, and in the Winter War. No combat losses of these vehicles have been recorded. They were largely taken out of service due to obsolescence of their armament. Even upon their creation, the RKKA saw them as a temporary measure until the development of superior SPGs.
The SU-76 prototype developed by factory #38 was also tested under the index SU-12, with a SU-76M indexed SU-12M.
SU-14
The SU-14 was developed in 1933, and a prototype was built in 1934. It mounted a 203 mm B-4 howitzer on a chassis made of T-28 and T-35 components. The B-4 was replaced with a 152 mm B-30 gun (ironically, the upgrade path in the game is the opposite).
The SU-14-1 was built on the superior T-35 chassis. The armament was a B-4 howitzer. The SPG was made ligher by reduction of side skirts from 10 mm to 6 mm. A variant of the SU-14-1, SU-14-Br2, was equipped with an armoured casemate and a Br-2 gun.
The SU-14 is in game, but again, not really. The tank that is in game right now is the SU-14-2. It was a SU-14, equipped with armour screens, to serve as a bunker buster in Karelia. A real SU-14 seems to be on its way in the next patch.
To make things even more confusing, the SU-152, developed under the index KV-14, is accepted into production under the name SU-14.
SU-15, SU-15M and SU-16
These two vehicles were proposed SU-76 variants. SU-15 was a SU-76 with a larger, fully enclosed fighting compartment, a S-15 76.2 mm gun, and GAZ-203 dual engines. The SU-16 was completely based on the production T-70, featuring a shorter hull. It was armed with the same S-15 gun.
SU-15M borrowed the semi-closed layout of the SU-16, while keeping the longer length, with dual GAZ-202 engines.
This is the end of the SPGs and TDs with SU in their name that were numbered sequentially.