Closure properties between two languages from different grammars We know that if we have two languages produced by one regular grammar, then any language produced from the union, intersection, and so on would be regular.

What if we have a regular grammar that produces language A and a different regular grammar that produces language B. Then could the closure properties still be used in order to produce another regular language C?

For example, is $A\cap B$ a regular language (intersection)? Is $A\|B$ a regular language (concatenation)?
A grammar produces exactly one language; it makes no sense to speak of two languages produced by the same grammar.

The closure properties of regular languages apply to any regular languages.