Both terms are used with identical meaning referring to shared leave pool instead of separate vacation and sick leave (“annual leave” is sometimes used for this purpose, but sometimes, e.g. federal service, equivalent to “vacation”); IME (which may not be representative) paid is somewhat more common than personal for the shared leave pool.

Confusingly, paid time off (with the same abbreviation) is also sometimes used in the more obvious sense encompassing all or most paid leave (including some or all of things like bereavement, company/public holidays, paid time for administrative shutdowns, etc.)

(All of this is in the U.S.)

No, it is "Personal." To differentiate from other types of paid days off that we get. (Bereavement, religious holidays, etc...)

And I'm also in the U.S.