I think that is a distinction without difference in as much as it's an excuse not to deal with it. But compatibilist "free will" must imply determinism unless some "magic" third alternative exists, because there isn't another option, and there is no evidence to suggest such a third alternative exists, so in practice every compatibilist I've had this discussion with have fallen back on arguing free will is compatible with determinism.

Definition doesn't tell all implications. In practice compatibilists do deeper analysis that reveals that determinism is required for free will.