There is a version for PS4 called Super Turbo Championship Edition, is it the same? And, it's possibl to do the glitches done in this version?

STCE is its own game. In the past, we have refrained from organizing runs of STCE due to problems with patching. Many different glitches were removed from subsequent patches of the game to the point that making an unbiased board didn't seem possible. Some new developments might make it possible.

In general, most of the movement tech and major glitches are possible on console versions of the game. However, the Select Door Glitch is not possible on console ports of the game. You should be able to abuse Save Point triggers, Swap Hop, Wall Hop, abuse El Infierno #3 and do other basic movement tech just fine.