What is the difference between 店 and 馆?
There is difference between 店 and 馆. Actually, it is likely be the convention of Chinese expression.

茶馆: a place where you can drink tea.

茶店: a place where you can buy tea, usually called 茶叶店.

咖啡馆=咖啡店，旅馆=旅店，理发馆=理发店

but 饭馆≠饭店，酒馆≠酒店