Not every context-free grammar is a regular grammar.
"A context-free grammar is a grammar in which the left-hand side of each production rule consists of only a single nonterminal symbol. This restriction is non-trivial; not all languages can be generated by context-free grammars. Those that can are called context-free languages."
Also, not every RG is a CFG
Again from Wikipedia
"In regular grammars, the left hand side is again only a single nonterminal symbol, but now the right-hand side is also restricted. The right side may be the empty string, or a single terminal symbol, or a single terminal symbol followed by a nonterminal symbol, but nothing else."
So the example in Cohen is indeed both a CFG and a RG, but it is not always the case that a CFG is a RG.
It also is good to remember that every regular language is context free, but not every context free language is regular. (To prove that a context-free language is regular, you need to use the pumping lemma.)