middle-ages and medieval are exactly synonymous. They are two different names for the time period and culture of Europe between the fall of Rome and the Renaissance. I suggest keeping Medieval as it is the overwhelmingly preferred term on this stack and in scholarly discussion in general.
ACTION: Once you've posted/read/analyzed the answers below and come to a decision, pro or con, please click the medieval tag. To the right of the orange "Watch Tag" button you'll see a list of links, one of which reads (currently), "Synonyms (1)". Click that link. Near the bottom you'll see a section titles "suggested synonyms:" Click the appropriate up-vote or down-vote arrow. If the vote gets to +4, the synonym is accepted. If it falls to -2, it's automatically deleted from the queue.