Frigates:
[snip historical BS]
The space based evolution of frigates has generally followed this concept of 'single mission specialization.' Epitomized by the popular and versatile Miranda-class, the frigate is often designed or refitted for specialized duties much like its maritime forebears. Transport and supply, defensive patrol, research and exploration and much more. In times of war, frigates are often utilized in support operations including patrolling and defending starbases and planetary system or protecting civilian shipping as well as a screen or reconnaissance for larger fleets. Frigates, while often the smallest class of capital starship, are still capital ships and despite their often single mission specialization, are still often capable of multirole operations even without a refit.
Destroyers:
[snip historical BS]
In modern Starfleet operations, a Destroyer class starship such as the Intrepid-class are capable of long term, independent missions and deployments and capable of handling multiple different operations such as defensive patrol, diplomatic presence and exploratory survey missions simultaneously. During fleet operations, the Destroyer class would provide both a screening element of the main fleet of warships as well as combat support as their array of torpedoes and phaser arrays as well as powerful shielding and superior evasive maneuverability would compliment the slower but more powerful cruiser class starships.
Cruisers:
[snip historical BS]
For the Federation, the Cruiser class is the most prominent and iconic vessel of Starfleet. The Excelsior-class exemplifies the space based evolution of the cruiser as a fleet vessel. Cruisers like the Excelsior-class are often used as flagships of Starfleet Admirals, serve as powerful tactical platforms for show the flag (and show of force) operations and are large enough to serve a vast array of Starfleet operations, with enough logistical capacity to fully serve in the roles of exploration, research, diplomacy and civil affair operations simultaneously. This is most recently personified in the Galaxy-class cruiser including Starfleets flagship, the Enterprise-D. Often its formidable array of weapons and powerful deflector shields cause others to define the Galaxy-class as a battleship but that would be wrong. A Battleship is a vessel dedicated to war. A more accurate term would be defining it as a Heavy Cruiser. While it is highly capable tactically, combat operations are not a Starfleet vessels specialty but simply one role of many.
Battleships:
[snip historical BS]
Starfleet notably does not currently employ battleships though after the tragedy of Wolf 359, there are plans of creating more tactically versatile Starfleet vessels or refitting current vessels with more offensive capabilities. Many Cruiser class vessels of Starfleet dedicate large amounts of its crew, power generation, and space to research, crew comfort, enrichment and exploration which during time of war can be rededicated to an increase of offensive and defensive capabilities. One often simulated theory is the concept of a 'War version' of the Galaxy-class starship which would be a dedicated warship, necessitating the removal of most civilians typically on board a Starfleet vessels, as well as everything from holodecks (except for tactical simulations of course) to astrometric labs. With minimal accommodations for a 'militarized' vessel, already large starships like the Galaxy and Excelsior-class could be updated with even more powerful shields, extra phaser banks and secure storage and deployment of even more potent photon and newer quantum torpedoes while the impressive sensor suits could be dedicated to scanning for enemy vessels for weak points in shields, or even laying out tachyon beams to detect the subtle distortions of cloaked starships.
Corvettes/Escorts:
[snip historical BS]
With the emergence of the Borg threat, the Federation soon floated the idea of a 'battle fleet' doctrine. Primary among this Battle Fleet would be a large number of 'Escort' class vessels, small dedicated warships solely meant to work in conjunction with larger Starfleet vessels in fleet battles similar to that of our shared maritime history. Recent 'official' advances in tactical technology, such as phase cannons, integrated nacelles, ablative armor plating and the evolution in tactical doctrine such as multi-vector attacks and simultaneous multiple targeting capability lend well to the development of a dedicated 'Escort' class. The main drawback however would be the assignment of Starfleet personnel to what is essentially a 'single mission' capable craft, that of warfighting.