Monseul“the best way to explain the difference”
I don't know if it's the best way, but providing contexts usually helps. Think of cases where 1) would come up in a conversation, but not 2). Conversely, think of cases where 2) would be used, but not 1). The difference in this specific case seems subtle, so it won't be easy.

Here's one possibility:
-- I didn't cook dinner Friday night. It was too hot.
-- How about Saturday?
-- No, I didn't cook dinner Saturday either. I stopped at a fast food place.
-- How about tomorrow, Sunday?
-- No. I'm going to a restaurant with a friend.
-- What about Monday? Will you be cooking dinner on Monday?
-- No. I'm invited to have dinner with the in-laws.
-- Gosh! Do you ever cook dinner? [Do you cook dinner? is not appropriate here.]
______
-- What sorts of things do you do around the house?
-- I do the dusting, and I polish the silverware.
-- Anything else?
-- I do the laundry, too, and clean the floors.
-- Do you cook dinner? [Do you ever cook dinner? might also be appropriate here.]
______
-- Who does the laundry in your home?
-- My daughter does.
-- Who takes out the garbage?
-- My husband does that.
-- How about dinner? Do you cook dinner? [Do you ever cook dinner? would be inappropriate here.]
-- Yes. I always do that.
______
These are just rough sketches of the sort of thing I'm referring to. I'm sure that, using these as a model, you will able to come up with better examples. 
CJ