For example: お礼として～　= As a token of gratitude, でも何かお礼をしたかったのよ　= But I just wanted to do something to show gratitude/say thanks (for a favor) 「ありがとう」は感謝の気持ちを伝える言葉です。　Thanks (Think of ありがとう as a normal "thank you" like in English. I hope this clarifies a little bit what the different is

お礼は　expressing appreciation. So お礼　including not only ありがとう but many kinds of expressing way, EX. giving a present, writing a letter, say something etc. ありがとうは　appreciate or thank you