What is the cardinality of the set of regular grammars?
There is at least one regular grammar per regular language, and all of them are pairwise inequivalent (for any meaningful equivalence relation). Since there is at least a countably infinite number of regular languages¹, that's a lower bound for the number of regular grammars as well.

Without loss of generality², you can write down every regular grammar as finite string over a finite alphabet. Therefore, there are at most as many regular grammars as binary strings, of which there are countably infinitely many.

Combine the bounds to get your answer.




The lower bounds follows from $\{a\}^n$ being regular for every $n \in \mathbb{N}$.
Encode all symbols using binary numbers.