An FDG PET/CT will tell if a cancer is using a lot of sugar. But, a PSMA PET scan will not - it looks for a specific antigen on the membrane of the cell.
An FDG PET/CT is not often used as an initial indicator for prostate cancer (unless the prostate cancer is in an advanced stage).
FDG PET/CT is regularly used for brain cancer (& some others) because those do thrive on glucose; prostate cancers are more affected by testosterone.