Yes, in most cases you can replace by байна - no problem.
But generally, I would explain the difference by following examples:
Чамд хэдэн төгрөг байгаа вэ? - Generally speaking, how much money do you have ? (in your bank account for example)
Чамд хэдэн төгрөг байна? - How much money do you have RIGHT now, at this moment ?
Би өдөр бүр дасгал хийж байгаа - I am exercising every day.
Би яг одоо дасгал хийж байна - I am doing my daily exercise RIGHT now.