Just looking at a list of active ships in any major navy right before World War 2 should prove the point that any "fleet" would become quite diverse in short order.
Older types remaining in service from earlier eras, newer types recently added to a fleet and brand-new models just coming into service; would all end up serving side-by-side.
In the US Navy (again, American bias!) prior to and during World War 1 - there were about 12 classes of Destroyers (alone) built and many were still in service in 1918.
Some of those WW1 Destroyers were still in service during WW2 - in addition to 13 newer classes built between the wars and during WW2. Again, just Destroyers... If you start looking at Battleships, Cruisers, Carriers, Submarines etc. - the list just keeps growing.