The Zorki 2C has a self-timer, which the Zenit C does not have - hence I thought it was based on the Zorki C, which is also sans self-timer. Whichever, it's essentially the Zorki with a mirror box/pentaprism. I've not used either of mine much - have you found the cords to break easily?
From an "anatomical" point of view, the Zorki 2-S (C) was the camera with mirror box that became the Zenit-S (C). The incorporated rewind switch into the shutter button collar (in the the Zorki-S/C, the rewind is still a separate lever) and the flash synch mechanism are two distinct features which the Zenit S got from the Zorki-2S.
Some other combinations:
Zorki-1 : Zenit (original)- same body shell, lens mount, and no flash sync.
Zorki-5 : Zenit-3 (both bottom loading, but flash synch is not the same)
Zorki-6 : Zenit-3M (both back loading, but flash synch is also not similar)
No Zenit SLR was based on the Zorki with slow speeds (3, 3M, 3S, 4, and 4K) because the slow speed dial already crowding the shutter speed mechanism left no room for the extra mirror actuating parts.
The self-timer from the Zorki 2-S was not installed in the Zenit S perhaps due to mechanical issues- the extra mechanism could no longer fit into the same shell, or perhaps because the delayed release will complicate the already intricate mirror release/ shutter blind release sequence during firing.
The cords are quite brittle, two of my three Zenit-S have already had their cords break. Replacement is a truly hellish affair. I used nylon braided fishing line for the replacement.
In contrast, the Zenit (-1) had a more reliable, albeit rougher, mirror system. It used levers and arms instead of the mirror and pulley relay. This was not too different from the latter systems used in the Zenit-3 or 3M, but the latter mechanisms had less parts. The arms and levers gave way to the cord and pulley to free the top for room for the synchro timing mechanism.