Informal vs Formal Acceptance (Graduate)
"Pending funding decisions" usually means that they are awaiting the results of grant and fellowship applications.

If you're applying to a university that does department-wide admissions, then they are probably trying to figure out the funding situation for the entire class before sending out the formal letters, since the formal letters normally specify the funding source as part of the statement.

If you're applying to a university where individual faculty members handle their own hiring, then they might be trying to figure out which funding source they will be using to pay your salary or stipend.

But usually a faculty member is not going to tell you "you've been admitted!" if they're not sure they'll be able to pay for you, so you shouldn't feel guilty about celebrating a little.