These two words are synonyms. The only difference is that you can not start a sentence with “ama” in written language. You probably hear the word ama more often than fakat in daily speech, especially young people tend to say ama instead of fakat . Also, there is a third word which is "lakin", but it is not that common. (http://www.learnturkisheasy.com/grammar/conjunctions)

ama :but fakat : however good luck.p

words "ama" and "fakat" came from arabic to turkish. and they have same means. just The only difference '' ama '' useful for youngers than ''fakat''. maybe you can watch some 'Green Pine' movie. you'll understand =)

Interchangeble. Ama is more oftenly used in colloquial language according to my humble observations.

to my knowledge there is no significant difference between fakat and ama. you can use them interchangeably. but youngster use ama more than fakat.