There is no difference and...
The inbox has always been "The global inbox". Certainly for as long as the API has existed.
So any inbox route will be Stack Exchange wide, even if it accepts a site
parameter. If you look at the doc for the /users/{id}/inbox/unread
route, it says:
This method is effectively an alias for /inbox/unread. It is provided for consumers who make strong assumptions about operating within the context of a single site rather than the Stack Exchange network as a whole.
It's not too clear what good purpose that serves. Maybe it's for developers who feel naked unless they send a site
parameter? 😉  (Except IIRC, extra parameters are generally ignored?)
Also, for almost every /users/{id}/xxx
route, there is a convenient shorthand /me/xxx
route -- where the user ID is taken to be the already authenticated user.
So we have:
/inbox/unread
~==~ /users/{id}/inbox/unread
by "alias"
/users/{id}/inbox/unread
~==~ /me/inbox/unread
by shorthand
- So,
/inbox/unread
~==~ /me/inbox/unread
Irregardless, they are de facto the same and have been since their introduction in API-2.0.