In my experience, references to a lead bet are consistent with the definition at pokerdictionary:
The player who makes the first bet in any given betting
round. This bet is always made on post-flop streets and when playing
out of position (OOP).
EXAMPLE “I check called the flop and lead the turn with TPTK, since it
was possible the cbettor would check back the turn with a marginal
Although maybe there's exceptions in some circles, I'm not used to the terminology being used as a noun (leader) but just as a verb. Calling somebody the leader could create some confusion in a tournament where a chip leader is a totally different thing. Also, using the definition as above, "leader" wouldn't hold much value as a descriptor because it doesn't carry over from street to street--on any new street any person can "lead the betting" when given the opportunity.
In both of your examples then, neither player would be the "leader" since it is preflop. Player A could "lead" the flop by betting in either case, but nothing player B does would be something we'd call a lead because they are in position.