I stumbled upon the following non-linear grammar
$$S \to AB$$ $$A\to aaA\mid \epsilon$$ $$B \to Bb\mid \epsilon$$
and the language generated by this non-linear grammar is {a^2nb^m : n ≥ 0, m ≥ 0} which looks to be regular. I was successful in drawing a DFA for this language.
Thus far, I have studied that Left Linear and Right Linear grammars classify as Regular Grammar and generate Regular Languages. I know there are certain Linear Grammars that can be converted to corresponding Left Linear or Right Linear equivalent forms. Similarly, I am guessing, we can write a Right or Left Linear grammar in a Non-Linear fashion and get the same regular language which is what is happening here.
Thus, what I understand is that Left Linear or Right Linear Grammars always generate Regular languages but a Non-Linear grammar may or may not generate a regular language. Is that the correct way to put it? Are there any gaps in my understanding?
Wkipedia states "an example of a linear, non-regular language is {a^nb^n}". Can I then say that above language is an example of non-linear, regular language? That sounds and probably is wrong.