As to the reason in "Metamorphosis" that there is no trail is that the entity disabled the propulsions systems and that created an overload to the shuttle power systems forcing them to cut all power.
KIRK: ..Building overload. Cut all power relays.
I suppose in hindsight, Kirk could of opened up one of the fuel valves and left a trail to follow. Then again, he might have thought that they needed to keep the fuel to escape from wherever they end up.
As far as differentiation from warp drive goes, I see no reason why the shuttle FTL system needs to be called Warp Drive. We know the nacelle equipped Romulan warbird from "Balance of Terror" has "simple impulse" and it was plenty capable of making that interstellar journey. For all we know, Impulse Engines and Ion Engines have nacelles as features for going FTL... It works just fine for TOS continuity. But for TNG's dilithium-regulated antimatter engines, that's a different continuity and I'd argue that most or all of the events in TOS didn't occur in TNG other than the basic concepts of their being the crew of the Enterprise under Captain Kirk, IMHO.