สัปดาห์ and อาทิตย์ hardly have no difference, in my opinion. We can SAY both in the same meaning (a week). For example, สัปดาห์นี้ฉันจะไปดูหนัง = I'm going to go to see a movie this week. อาทิตย์นี้ฉันจะไปดูหนัง = I'm going to go to see a movie this week. Anyway, อาทิตย์ this word can also refer to "Sunday (abbr. วันอาทิตย์)" Note : We are more likely to use สัปดาห์ in written language. I often see it on a newspaper, a book, etc.) Hope this help :)

สัปดาห์ is just more formal than the colloquial อาทิตย์. This is similar to using annually versus yearly, they both have the same meaning.