The two phrases have the same meaning with a small nuance difference.

 

* kamsahamnida (감사합니다) = most common way to say "thank you" to someone outside of your close circle.

* komawoa (고마워), komawayo (고마워요) = more casual than 감사합니다.  고마워 is a plain form to use with friends, while the more polite 고마워요 can be used broadly like 감사합니다.

고마워 sounds more friendly, so you prefer it for your friends, siblings, or any children. 감사합니다 will sound too formal for them. 

For family members or relatives who are much older than you, 고마워요 would be good.  In all other cases, 감사합니다 is the best.