The main difference was that warp power could be regenerated whereas impulse was a fixed fuel quantity.
Was warp power really "regenerated"? The only time we hear of power regenerating, it is with respect to life support power in "Mark of Gideon" - which could simply mean that the fuel supplies of warp drive would last forever when gradually used for recharging the batteries of life support for just two people.
In TOS it appears that the warp power was being regenerated. We have:
"The Mark of Gideon" - After Kirk slows the warp engines to sublight:
KIRK: Well, let's see. Power, that's no problem, it regenerates. And food. We have enough to feed a crew of four hundred and thirty for five years.
"Where No Man Has Gone Before" - Burnt out warp engines were regenerated with new parts.
"The Naked Time" - all engines shut down cold and it takes 30 minutes to regenerate them to full power.
"By Any Other Name" - a several thousand year trip to the Andromeda galaxy was seen as a problem of time, not fuel.
Whenever the warp power was severely taxed or drained, it would take time to build them back up again, or "regenerate" them. This occurs in "The Tholian Web" and "Tomorrow is Yesterday". More specific problems could be when the dilithium crystals were not at full power, requiring re-amplification. This occurs in "The Alternative Factor" and to some extent as well in "Day of the Dove" and "The Voyage Home" when the crystals start to deteriorate.
While TOS writers probably had wild ideas about how warp was fueled or how it worked, none of those were so explicit as to contradict the later, more explicit movie or TNG era deas about antimatter annihilation and hydrogen-antihydrogen tankage and whatnot.
As far as I know, the TOS movies were inline with what was depicted in TOS. What specific examples were you thinking of?
TNG and it's continuity however does have fundamental differences (contradictions) with how dilithium and fuel work.