Are regular grammar languages defined from "accepting" states?
There is a one-to-one correspondence between NFAs and right regular grammars without productions of the form $A \to a$.
Given a right regular grammar with productions of the form $A \to aB$ and $A \to \epsilon$ and starting symbol $S$, create an NFA in which:

The states are all nonterminals.
The initial state is $S$.
A state $A$ is final if there is a production $A \to \epsilon$.
There is an edge labeled $a$ from $A$ to $B$ if there is a production $A \to aB$.

This NFA accepts the same language as the grammar.
You can also easily carry out the transformation in the other direction.
This shows that in the absence of rule of the form $A \to a$, the analogs of accepting states are nonterminals with productions of the form $A \to \epsilon$.
We can replace a production $A \to a$ by a pair $A \to aX$, $X \to \epsilon$, where $X$ is a nonterminal which is common to all such productions, but doesn't appear anywhere else. We can think of $X$ as the accepting sink. A production $A \to a$ signifies a possible transition to the accepting sink.