The problem with natural consequences is that sometimes they are too abstract or too distant in the future for children (and most adults too) So that's where logical consequences come in -- where the adult steps in to provide a consequence. But it must be relevant, reasonable, and respectful. So in the teeth brushing example - taking the bike away for not brushing would not be relevant. Forbiding candy for the next 5 years would not be reasonable. Saying anything with a loud, angry, shameful voice would not be respectful. In my book that's what turns a consequence into a threat. If you are not respectful or if you repeat yourself over and over without follow through -- that turns a consequence into a threat.
In our house, teeth brushing will happen. The choice is "do you want to hear me tell a story while I brush or not" If the child is agreeable and calm they get to hear the story. If not, "well, looks like we can try again tomorrow to hear the next bit of the story" DH tells great stories and they always want to hear more, so they are motivated. Now telling stories has nothing to do with teeth, but he can't tell the story if they are too noisey or too wiggly, so it has everything to do with their behavior. And he stays calm, doesn't shame or lecture. Just states it.
Your second example, the natural consequence of hitting is not just pain, but the other person may not trust you or want to play. That can be explained, but is hard to follow through on. But your second example is a good logical consequence. Actually leaving the play date might be unreasonable for a single hitting incident with very young children, but leaving the space, calming down, etc if fair. And if behavior is truely unappropriate, I would leave. I make sure they know what behavior is expected before the situation and then "We have to go now because you are choosing to do blank." No reprimands or shaming, just calm and firm.
So no, i don't think it is just semantics. Threats might look a lot like applied logical consequences but be too harsh, applied in an angry way, or empty words. check out positive discipline for the preschooler