Moving at 10+ in TOS was always due to some alien influence or something. The Enterprise engines were definitely not capable of those speeds under normal conditions.

With that said, in TOS, warp 10+ is just “you are moving really fast”. But in VOY, warp 10 is “you are literally occupying every point in space simultaneously” and there is nothing past warp 10. It is a complete reimagining of the ceiling to warp speed. In TOS, it seemed there was no theoretical maximum warp speed, just like how there is no theoretical maximum to kilometers per hour. But by VOY, warp was capped at 10, and once you reached that speed, you became a salamander because reasons.

The best fan explanation for the retcon that I have seen to justify why the scale appears to differ in-universe is that they are genuinely different units. That at some time between TOS/VOY, scientists made some new breakthrough in their understanding of warp mechanics and discovered that there actually was a ceiling to warp speed. As such, they decided to change the standard warp units, making “warp 10” this new ceiling and everything else is just a fraction of that. According to this logic, when Scotty says “Wow, we are traveling at warp 30!” he is speaking in TOS-era warp units, which might translate to just something like “warp 8” in VOY-era units.