While reading through the conditions described in Appendix A of the 5e PHB, I realised, that some of them say a creature "can't move" (e.g. Stunned, Unconscious), while others state that its "speed becomes 0" (e.g. Grappled, Restrained).
Can anyone explain to me the mechanical distinction between these two phrases?
Best Answer
Under some conditions, a speed that has "become zero" can be increased magically, as discussed in this question.
If you "can't move", then changes to your base speed have no effect.
Also, "can't move" does not imply "can't take an action". This is indicated by the fact that all conditions that use the phrase "can't move" include the condition Incapacitated in their description, which specifically prohibits actions and reactions.
The spell Magic Jar (PHB p.257) gives an example of a case where you can't move, but you can take an action:
On the follow up:
Technically? Yes, I believe so. Mechanically? Not as far as I can tell.
From both a linguistics and RAW perspective, "can't move" sounds like "cannot take the move portion of their turn", as in the PHB p. 189:
While "speed becomes 0, and it can't benefit from any bonus to its speed." sounds like you can use your move, but you can only go zero feet and nothing can increase that distance.
The only case I can imagine where these would not yield the same in-game results is if there were a way to use your move to cause an effect while still spending no more than zero feet of your movement. I have yet to find such a case. There are spells that spend feet of movement like currency, such as Tree Stride (PHB p.283), but I have found no instances where one can cause an effect using 0 feet of movement.