* Corvette/Frigates -- Smaller ships with smaller munitions. They're just missile platforms. Anything smaller than a Corvette basically is ignored for most discussions. Frigates are slightly larger than Corvette.
* Destroyers -- Bigger than Frigates. Not only do Destroyers have significant missile capacities (like Corvette / Frigates), Destroyers are big enough for major sensor suites. SONAR, RADAR, etc. etc. Maybe enough for a CWIS (aim-bot with a gatling gun, designed to automatically shoot down enemy missiles as they approach).
* Cruisers -- Bigger than Destroyers. More missiles, more sensors. While a Destroyer might have 1x CWIS and 1x RADAR, you might be seeing 2x or 3x CWIS or RADARS on the larger Cruiser class.
> In these days and age where all war ships seem to be essentially floating missile launch platforms, what is the difference?
Defense. You need a lot of power to run those RADAR systems, which are constantly scanning the skies for enemy missiles. Corvette/Frigates are too small to have a CWIS / anti-missile defense system, so they need to hang around larger ships (like Destroyers or Cruisers) for defense.
Multiple Destroyers could be stationed next to each other to increase their defenses. But if two Destroyers were just going to sail together (for better RADAR coverage and/or defenses), its a better idea to just make a slightly bigger ship, but with twice the RADAR / twice the defense of a singular Destroyer.