The main difference is that fluently is an adjective and smoothly is an adverb. Fluently is most often used when to speaking and reading. But smoothly is used in many different contexts in daily life. eg - the gate opened smoothly Fluently - speaking or writing with ease Smoothly - easily and without interruption or difficulty

That's an interesting question. I would say that fluently is used mainly to describe language skills, whereas smoothly can be used to describe many other things in addition to language skills. Also, fluently implies a mastery of language skills; whereas smoothly is a bit more vague. Smoothly makes me think of the sound of the language output rather than the overall mastery of the language.