Soviet aerospace development involved Design Bureaus (abbreviated as OKB in Russian). The OKB are very roughly analogous to Western aircraft companies in that they had were fairly self-contained and would have requirements passed onto them by the government for competition. OKBs generally specialized in certain areas, and often times politics would play a part in procurement. In general, the trend through the Cold War was that Tupolev was specialized around bomber development, Ilyushin around transports, Sukhoi around interceptors and heavier tactical aircraft, and Mikoyan-Gurevich around frontal aviation. Yakovlev fell more into trainer aircraft following WW2, although we also see them have some niches with VTOL aircraft (Yak-36, Yak-38, and Yak-41) as well as some long-range fighters and a failed bid at the contender for what became the Su-27/MiG-29.

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It really depends on the era you're looking at, but in general, we see that the wide variety of aircraft employed was due to the wide variety of roles. If we're looking at the era when Yakovlev, Sukhoi, and MiG all had fighters in active service by the VVS (Soviet Air Force) and PVO (Air Defense Forces), then we see a very wide variety of fairly specialized roles in outwardly very similar aircraft.

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The MiG-15, -17, -19, and -21 were (relatively) simple designs that, while optimized for interception over taking on enemy fighters, were more rugged and better suited to frontal aviation (VVS-FA) than more complicated interceptors. The MiG-19 was largely overshadowed by the more capable MiG-21 and easier to operate MiG-17, but in general all these MiG types were operated in large numbers by both the VVS and PVO, with VVS examples being shifted to tactical aviation roles as they became obsolescent. The MiG-17 in particular persisted for a while as a tactical bomber after the MiG-21 had taken over more traditional fighter roles. Although these aircraft did see significant use in the PVO as well, a lot of the development behind the scenes sheds light on a lot of their shortcomings in the interceptor role. A good deal of effort was put into development of all-weather fighters and radar-equipped variants (particularly of the MiG-17), but these efforts either fell through or were limited-capabilities stopgap measures. Of these MiG models, the MiG-21 was the most successful one to feature a radar (MiG-17 onward had gun-laying radars and some MiG-17 variants in PVO service had very simple radars), but even its radar was very limited in capabilities. Early production (MiG-21F) featured only a rangefinding and gun-laying radar, and the MiG-21PF that did feature a more advanced radar was still very limited due to the size of the radome. All the MiG types also suffered from poor range and endurance, causing problems for the PVO (which needed to patrol vast stretches of airspace) and both tactical aviation among the VVS and foreign operators.

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Sukhoi was a bit of a mixed bag. The Su-9 and -11 were very specialized interceptors, designed from the ground up to carry semi-active radar-guided missiles. Although they were nearly identical to the MiG-21 in appearance, they had better radars and were exclusively operated by the PVO. These designs still suffered from a lot of the shortcomings of the MiG-21 in PVO service (short range and poor quality radar), so Sukhoi followed it up with the larger Su-15. The Su-15 was a much larger two-seat aircraft with a significantly larger and more capable radar. It was a specialized interceptor that offered a significantly longer range than the MiG-21 or Su-11 with similar performance and a better payload of missiles. While PVO interceptors were always heavily reliant on ground control, the second crewman also was a major step up, as it massively reduced the pilot workload (historically a major issue on Soviet fighters). The Su-7 was an outlier, procured as a tactical fighter alongside the MiG-21 to fill the same role. It ended up being redirected at the end of development as a fighter-bomber, and in service it would have a fairly successful career as a tactical strike aircraft, eventually being developed into the swing-wing Su-17/22 strike aircraft. Unlike the MiG-21, the Su-7 was purely a frontal aviation platform.

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Yakovlev's fighters around the same time were even more specialized. The Yak-25 and Yak-28 were long-range aircraft primarily intended as interceptors for the PVO. The Yak-25 was a twin-engined fighter equipped with a radar and a dedicated radar operator and a range longer even than the Su-15. The Yak-28 was a supersonic improvement of the design along the same general concept, but with the ability to fire radar-guided missiles. Both also had niche variants developed, including reconnaissance and tactical bomber versions. Although I haven't ever really found specifics on the bombing capabilities of the Yak-28 variants equipped as such, the details I've been able to find give the impression of it being roughly analogous in role to the American F-105 (as originally designed).

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One thing to note is that the OKBs weren't necessarily stovepiped into their niches, although politics very much did come into play at times. Tupolev managed to briefly usurp Yakovlev's hold on long-range fighters with the Tu-128, only for MiG to take it over later with the MiG-31. Yakovlev put in serious contenders for many of the Soviet tactical fighter programs even up to the MiG-29 and Su-27, and Sukhoi very nearly beat out Tupolev for what became the Tu-160.

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If you're referring to a different time period, however, let me know, and I can elaborate on some more detailed development decisions of certain Soviet aircraft programs.