Every stage in ST/SFIIX is different on actual CPSII arcade and on emulated CPSII. So if you play GGPO or Supercade online then you will be able to see that the stages are indeed running at different speeds. If you play using something like MAME or FBA offline then you will encounter stage speed differences as well. Just like an actual arcade board. The order of fastest to slowest stage speeds is consistent from what I remember for each regional version of arcade ST and for all of the various emulators. The thing is that most, if not all, of the emulators run ST overall faster compared to the original arcade board. So the same stage on arcade ST is much slower than the same stage on MAME or FBA or GGPO (providing the speeds are the same setting).
T0 is slowest speed and T3 is fastest (T1-T4 on the USA/World boards). Also T0 is not actually zero speed compared to something like CE or Super, it's actually a 'turbo' speed that skips over frames of animations. T0 is kind of misleading if you've only played ST and nothing else. Some of the console versions of ST actually have a zero speed setting that is the same speed as CE or Super and does not drop frames (HDR has this for speed zero for example).
As far as console ports go, most of them have one constant speed for all stages per speed setting, so T1 is the same on every stage, T2 is the same on every stage, and so on. This is how the DC version of ST runs, PS2 AE, and how HDR Remix and Classic Run, amongst others. CCC2 is one of the few versions however which has different stage speeds, as that version was emulated CPSII on the PS2, based off of an ST rom file. CCC2 has many known issues that make the game unplayable and stage speeds and other speed settings happen to be one of them. So the one console version where arcade speeds were attempted to be replicated ended up having that goal cause tons of problems.
Stage speeds are important at competitive levels. Getting a stage like Dhalsim's or Zangief's versus Blanka's or Ryu's can noticeably change the timing for lots of things. You need to constantly be adjusting on the fly in ST because every stage has different timing. It's yet another dynamic that arcade ST has that many other games do not share. Grand Master Challenge indeed.