This division (objective vs. non-objective) is highly relevant for English morphology.
The same verb lexeme can enter more than one of the outlined classification sets (the subclass migration of verbs):
Who runs faster, John or Nick? – uncomplementive.
The man ran after the bus – adverbial complementive, non-objective.
I ran my eyes over the uneven lines – adverbial objective, transitive.
And is the fellow still running the show? – monocomplementive, transitive.
The migration forms in the area of notional subclasses proper may be interpreted as cases of specific syntactic variation. For more cardinally differing lexemic sets (e.g. functional vs. notional) this kind of differentiation may be analysed as lexico-grammatical homonymy.