Yashica build all of the Contax cameras, quite a few of which were also sold in Yashica 'colours' (which includedthe use of cheaper materials, plastics instead of metal casings, etc.).
You're right, of course, Yashica undertook the manufacturing lead for both Contax and Yashica lines, and nowhere was the commonality more evident than in the manual SLR lines, which shared a mount and in some cases accessories like autowinders. As far as I know, none of the Yashica SLR lens designs are Zeiss, and there's no truth in the stories sometimes put about that Yashica ML lenses were those from the Contax line that didn't make the stringent Zeiss QC standards ; and in any case, Yashica had a rather impressive pedigree of their own.
The Contax and Yashica T lines are both aimed at the P&S market, but at very different strata, and the Yashica T line isn't a Contax T just pared back or of cheaper materials (though they are not as solidly made). The Yashica T range are equipped with Tessars, and the Contax T range have Sonnars. My Yashica T5 is a pure point and shoot ; just about the only manual control you have is the ability to force the flash to off mode for the next picture. You have no control over the exposure, not even the exposure compensation, which is entirely automatic and silent, and you have no idea what the aperture or shutter speed may be. My Contax T2 is quite different in design. Whilst it's an auto point and shoot, I can set any aperture from f/4 to smaller, and have a read-out (admittedly only ballpark) of the shutter speed in the viewfinder. It has an autofocus mode, but I can over-ride that with manual focus selection. The T2 offers full control over exposure compensation.
The Yashica FR could be seen as a pared down RTS, but the Yashica T cameras can't be seen as pared down versions of the Contax T line. As far as I know, the last model in the Contax line was the T3. There was a TVS, with a Vario-Sonnar lens around 28-56mm, and I'm pretty sure there was a Yashica T zoom with a Vario-Tessar lens.
The Yashica and Contax AF SLR lines completely diverged, and have nothing whatsoever in common. There's nothing interchangeable at all between them.
The Yashica T5's Tessar performed way beyond my expectations. This was brought home to me after we returned from a trip to Italy, and I had a stack of films processed. I'd had all my colour negatives processed with 6"x9" prints, and a great many of the packs had been shot at Pompeii and Herculaneum. As I went through photograph after photograph, I kept exclaiming to my wife how superb the Contax Planar 50mm was, until it began to dawn on me that the pack of prints I had on the desk in front of me didn't have a mix of wide and medium tele shots. A quick check against my photo notebook confirmed that I'd been looking at one of the T5 films, and it was good enough to make me mistake it for one of the Contax SLR packs. Incidentally, my experience with the Yashica T3 was completely different, I couldn't get a decent shot out of it, but as others write highly of it, I'm prepared to believe I really did have a lemon. But the T5's reputation, even if it has acquired cult status, is built on merit. However, there is absolutely nothing of similarity between models in the Yashica T and Contax T ranges. If they didn't use the letter T, you would not have any way of pairing them either in design or functionality.