Yes, they mean the same thing as far as the activity is concerned, but there could be a difference with regard to the “type of person” doing it. “Tagapag” could mean someone who does it as a profession or is specifically assigned to perform the task.
For example: “taga-al
aga” may be anyone taking care of another person, but “tagapag-al
aga” might refer to one employed as a caregiver.; “tagal
uto” is someone who does the cooking by default, but “tagapagl
uto” might suggest that it is a task assigned to a particular person.
The differentiation is not rigidly applied though and some might still use the words interchangeably. At times, the context may be the one to indicate the distinction.
Also, the 2 prefixes may not always be applicable to or may not provide the same meaning with the same root word.
Tagak
ain – a word we use to mean one who eats what others won’t or won’t anymore, e.g., leftovers, meat in the company of vegans. There is no “tagapagkain”.
“Tagap
ágsalit
á” is a spokesperson, but “tagasalit
á” might suggest one who presumptuously takes it upon himself to speak on behalf of another and as such, may suggest inappropriate behavior.