Difference between $F_2^n$ and $\Bbb F_2^n$ for a field
Some authors write $F_q$ for the finite field of order $q$.  Some authors write $\mathbb F_q$.  Some authors write $\mathbf F_q$.  Unless there's a typo, or unless your pet author is particularly confusing and as a personal peculiarity makes a nonstandard semantic distinction between them, which one you use is a matter of taste.  And as we all know—de gustibus non disputandum est: only with gusto can taste be argued.

What parts of the text you are reading are leading you to a state of confusion?  Maybe you can ask a question about those in particular.