สัปดาห์ and อาทิตย์ hardly have no difference, in my opinion.
We can SAY both in the same meaning (a week).
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 :)