is going to cook vs. is cooking

[PINKGREAT]

Do they mean the same thing?

[Casiopea]

It depends on the context.

Context #1
She is cooking right now.
=> She is making food right now.

Context #2
She is going to cook right now.
=> She is preparing to cook / She is just about to start cooking / She hasn't started cooking yet.

Context #3
Mother is cooking breakfast for us tomorrow.
=> Future meaning: She is going to cook breakfast for us tomorrow.

Note again that, in expressing the future, be going to + base verb is often shortened to be + base verb + ing.

EX: She is going to cook tomorrow => She is cooking tomorrow.