What is the principle difference between determinism and nondeterminism as it pertains to finite accepters?

A deterministic $$ returns a set of states, a nondeterministic $$ returns a state.

A deterministic $$ returns a state, a nondeterministic $$ returns a set of states.

$$ transitions are required for determinism, they are not for nondeterminism.

$$ transitions are required for nondeterminism, they are not for determinism.