There is also a different meaning for "cook up" not relating to food. "cook up" is sometimes used to describe making something suddenly or without a plan. For example: If your wife asks why you were late coming home from work, and you dont want to admit you stopped to drink some beers with friends, you might have to "cook up" an excuse.

They are the same meaning. However, "Cook up" is a more colloquial, more playful way to say "cook". for example you can say: ✅ "I'm going to cook up some eggs" or ✅ "I'm going to cook some eggs" and it has the same meaning. Also "Cook up" must be followed by a noun, while "cook" does not, for example ✅ "I'm going to cook tonight." but you CAN NOT say: ❌ "I'm going to cook up tonight"

I agree with David but in British English cook up can also have a more negative meaning of doing something that's not quite the right way of doing things or maybe even dishonest...so you might say, I'm going to cook up (make) a plan or I'll cook up some excuse to get rid of her. We also have the expression 'to cook the books' which is when you are being dishonest in your business accounts. These expressions are colloquial and a bit playful.