As with any periodization, they are defined by convention and exist for convenience. I've never heard of any set boundaries for "ancient," as it's usually more of a description than a period. Post-classical in western Europe has a nice solid end date at the sack of Rome, but one could use it differently for different lost territories of the empire. Modern will have a different beginning for every field in every region.

All the terms say is "these things are more akin than those things." If I call Seneca and Vergil classical Latin writers, it means they have more in common with each than other with St. Jerome's Vulgate. While Jerome translated this Bible before 476, it's a typical example of medieval Latin; it was in common use for centuries after. When historians undertake studies comparing two period, we aren't looking to set a date before and after which things are different. We look for the forces and processes of change, possibly identifying individual actions, movements, or events as "modern" or "pre-modern" along the way.