Frigate being the smallest and least well armed to the Cruiser being the heaviest and best armed (beside the historical battleships and pocket battle ships (a kind of extremely well armed crusier) of course).
Frigates generally have anti-submarine and a light escort focus as their main tasks, with a capability in the anti surface and anti air roles, but with a lesser degree of capability than larger ships.
Destroyers are normally anti-submarine, anti-surface and anti-air capable and perform all 3 of these roles to a high degree of capability. Cruisers normally perform anti-surface and anti-air to a high degree of capability, but with only a lesser degree of capability or focus on the anti-submarine role.
Frigates these days weigh anything from 2000 - 5000 tons, Destroyers are in the range of 5000 - 8000 and cruisers normally 8000 tons and above. Few Navies actually operate ships as capable and as large as Cruisers these days, with most forces concentrating their surface action forces on Frigates, with perhaps a few destroyers. Modern heavily armed Cruisers are beyond the realities of funding for most Navies these days...