There is actually an OEM Canon ultrawide zoom lens that costs less than all the lenses you're looking at. That is the EF-S 10-18 f/4.5-5.6 IS STM, which is the low-price alternative to the Canon 10-22.
Yes, the Samyang and Rokinon (and Vivitar, Pro-Optic, Opteka, Bower, Phoenix, Walimex, etc. etc.) are the same lens, and are optically identical, although not identical in outward appearance. However, Samyang's lenses are manual-only and do not perform electronic communication with the camera body. You have to manually focus, and manually set the aperture with the lens's aperture ring. You can only use M/Av modes because the camera body can't control the aperture. You have to use stop-down metering (i.e., the view through the viewfinder goes darker the more you stop down). The EXIF won't have any lens information (aperture used, lens name, etc.) in it. What you save in dollars, you will pay back in inconvenience vs. a lens that can communicate with your camera body.
You also won't have much luck in getting a lens that's ultrawide on both crop and full-frame because of the crop factor. While 14mm is ultrawide on full frame, it's the full-frame equivalent of a 21mm lens on a crop body. This is the single category of lenses where you would probably be much better off getting a crop lens, and then reselling it when you move to full-frame, because none of the ultrawide offerings for full frame are ultrawide on a crop (ok, maybe the Sigma 12-24), none of the crop ultrawides cover a full-frame sensor even if they still mount, and the crop versions cost quite a bit less.
The Tokina 11-16, btw, is a crop lens and will vignette on full frame up to about 15mm. That's why Tokina also makes the 16-28/2.8 for full frame.