Conversational fluency is the ability to interact in foreign language conversation. Therefore, it only requires a command of the language sufficient enough to convey a message, be understood, and comprehend the response, i.e. carry a basic conversation. You may still make errors in grammar, syntax, or word choice and you may still have to plan and think of what you are saying or how to say it, but you would still be considered conversant if you can do this at a relatively fluid pace with limited pauses/breaks and the other person can comprehend with minimal difficulty. At this level, you should be able to carry on everyday conversations and even make do in an immersion setting.
Fluency in a language is achieved when you can speak the language without breaks in fluidity, meaning that you no longer have to pause to think of the proper conjugation or word order, etc. The language is so well learned that you no longer have to actively think about/plan your sentences. Further, this should be the case in all components of language (reading, writing, comprehension, and speaking) to be considered completely fluent in a language. Often, reading and writing are more easily mastered than auditory comprehension and fluent speaking. Another difference between a conversational vs fluent language mastery is the proper usage, understanding and command of word nuances/connations as well as idiomatic phrases. Thus, being fluent is a bit more involved than just being able to carry on an everyday conversation.