Ama and fakat mean exactly the same but no sentence can start with ama in written language and somehow older people use the word fakat more and I do not remember any black and white Turkish movie using the word ama :) hope it helps

There is no difference in the meaning. Just "ama" is more common. There are also "lakin" and "ancak" which have the same meaning but these are not used in spoken language at all. You may see them in books or stuff...

AMA often not used in formal speech and writing, it is an informal phrase. FAKAT used in formal... meaning same. two of them arabic origin words.

"ama" and "fakat" are exactly same for english "but". But, we're using it in another meanings. e.g strengthening a adjective e.g bugün hava çok sıcak "ama" yağmurlu. (you can use "fakat" here. there will not any change.) bugün hava çok "ama" çok sıcak. (you can not use "fakat" here.) i use "ama" for strengthening an adjective (çok)

Herkese teşekkürler! ^-^