So, in the Napoleonic War era of Hornblower, Ships of the Line Of Battle (later abbreviated to "Battleships") were 1st, 2nd, or 3rd rate. Frigates were 4th or 5th rates, Sloops, Snows (rhymes with cows, not crows), Barks, Brigs, and all the other non-SHIP vessels were 6th rate. Frigates were the biggest ships to lie outside the Line, and the most versatile. Battleships went to a station, then stayed there for a deployment, as part of a group. Frigates were assigned in groups and individually. Frigates sent on an independent deployment, or cruise, became known as Cruisers.
So Kirk's Enterprise was definitely NOT the biggest thing Starfleet had. it was the biggest and best ship sailing solo on independent operations. But bigger, better, more capable battleships (with tighter leashes), bigger, better, more capable research ships (with watchdogs), and other types should also exist.