감사합니다 is Sino-Korean. The characters are: 感謝 고맙습니다 is pure Korean.

In addition to this wonderful explanation. Be aware that the ㅂ-ㄴ combination in -ㅂ니다 Is pronounced like m-n instead of b-n. Also the 고 in 고마워요 sometimes goes in the direction of ku instead ko but this last part is no rule just an observation

Irina, I can't give you a thumbs up. So I just want to tell you that that was a very comprehensive explanation!! Nice!

Thanks a lot for the help to all of you! 고마워요!! :)

as 감사합니다 is of Sino-Korean origin, it is _slightly_ more official and _slightly_ more honorific comparing to 고맙습니다 (like all Sino-Korean words comparing to pure Korean words). so you'd rather hear 감사합니다 in official situations or for more official relationships. except of this, the usage will depend from personal preferenses of the speaker. gradation from formal to informal would be: 감사합니다 --> 고맙습니다 --> 감사해요 --> 고마워요 -->고마워 --> 고맙다. hope my comment was of some help ~