First of all, I declare that I am a student who knows a little about music score. The following information is based on online information and my own experience, for reference only:

As far as I know, F definitely means strong, and P means weak.

then, LZ, where did you find the information? When I searched for Protissimo, I found only a piece of information, which still introduced Prontisimo, with an N more than Protissimo. If it's Pretissiomo, it's for speed, which means "the most urgent board" and has nothing to do with strength.

the complete spelling of "f" is Forte, the complete spelling of "FF" is Fortissimo

the complete spelling of "p>"F is Piano, and the complete spelling of" PP "is Pianissimo

These words all come from Italian. Baidu Encyclopedia says it comes from Latin, which is wrong.

LZ If you want to know more, you can look at Wikipedia's "Strong and Weak Method". If you are good at English, you can look at Wikipedia "Dynamics(music)". I won't post the link for fear of being swallowed.