Except they're "different" in terms of how you characterize a single underlying principle, which is that "physical harm is being received." I noted elsewhere that this was akin to an order of operations, where the game rules takes you "down" to a certain level in that order, and then you have to take up the work yourself until you reach the level of contextualization you want:
- Hit points have been restored, indicating damage has been healed.
- Characterize the restoration in terms of the amount of hit points recovered versus the total hit points remaining and/or their maximum hit points.
Contrast this with what happens when you don't grant the premise that there's even any damage happening:
- Hit points have been restored.
- Determine if this is a healed injury or a replenishment of stamina.
- Characterize the healing in the context of A) hit points recovered versus total hit points remaining and/or their maximum hit points, or B) in terms of why they've regained stamina.
So essentially, you've taken a two-step process and turned it into three steps; three-and-a-half if you look at the third have an A and B option that need to be parsed. That's a larger gap that you, the player, have to then bridge, because there's more than needs to be determined.
So yes, hit points have always required some contextualization; I never said otherwise. But the degree to which it walks you through the process before leaving the work to you is different in 4E than it was in earlier editions.