SRT is just text and timings. It includes no other information - font, color, drop shadow, size, etc. are all determined by the player you’re using.

SUP is the Blu-Ray subtitle format if I remember correctly. It’s not text - it’s images. So the font, size, position, drop shadows, color, etc. is all embedded in the subtitle file itself and can’t be changed (except maybe size and/or position) by your player.

Otherwise, yeah, they should both be used in the same way. If you’re authoring a Blu-Ray with subtitles, definitely use the SUPs since the SRT files will have to be converted by the software to SUP anyway.