> It may sound like executing your specification, but it is a bit smarter,

It's more than just "a bit smarter" I would say, and explicit state enumeration is nothing at all like executing a spec/program. For example, TLC will check in virtually zero time a spec that describes a nondeterministic choice of a single variable x being either 0 or 1 at every step (as there are only two states). The important aspect here isn't that each execution is of infinite length, but that there are an uncountable infinity of behaviours (executions) here. This is a completely different concept from execution, and it is more similar to abstract interpretation (where the meaning of a step isn't the next state but the set of all possible next states) than to concrete interpretation.