To me, an "explorer" is just a term for a very large, long-range Starfleet vessel ideally suited for deep-space operations. But like most Starfleet vessels, it's can carry out a variety of different missions when necessary, IMO.
Based on a system I adapted from a website whose name I can't remember and who I can't seem to find anymore, I have come up with the following for my own fanfic:
Explorer type: Largest starships in Starfleet. Equivalent to the capital ships of today's navies: aircraft carriers.
Sovereign-class,
Galaxy-class, and
Nebula-class. Capable of long-term independent operation and typical command ships during wartime. Perfect for deep-space exploration, independent long-range tactical operations, first contacts, and other diplomatic functions.
Heavy cruiser type: Used to be the largest starships before the explorer type came into being. Capable of medium-term independent operation.
Akira-class,
Niagara-class,
Ambassador-class,
Excelsior-class. Used to be capital ships. Well-suited for deep-space missions, independent medium-range tactical operations, first contacts, and other diplomatic functions.
Tactical cruiser:
Prometheus-class. Just like it sounds.
Light cruiser: Smallish, fast, well-armed. Perfect for short-term deep space missions, independent short-range tactical operations, first contacts, and other diplomatic functions. All of the power and ability of an explorer without the size or needed resources.
Intrepid, Sabre, Cheyenne, Renaissance, Wambundu, and
Constellation-classes.
Destroyer type: Well-armed, not as fast, medium exploration capabilities. Well-suited for long-term survey missions after initial deep space mission has passed. Also good as escorts or cargo couriers.
Apollo, Hokule'a, Miranda-classes.
Frigate type: Lightly armed, fast. Perfect as escorts or cargo and personnel couriers. When someone says, "We need to get there fast and it's dangerous," they're asking for a frigate or a light cruiser.
Norway, New Orleans, Steamrunner, Merced-classes.
Medical frigate:
Olympic-class. Just like it sounds. Frigates escort them.
Scout type:
Freedom and
Centaur-classes. Fast, short-range. Work well as patrol craft.
Escort type:
Defiant-class. Unofficially, she's a warship.
Surveyor type:
Nova and
Oberth-classes. Perfect for long-term, in-depth surveys (ha!) of planetary systems or sectors.
Transport type:
Istanbul, Yorkshire, Sydney-classes. Personnel or cargo.
Freighter
: Antares-class.
Runabout:
Danube-class. Short-range surveys, escorts, personnel transports, and short-term research/surveying assignments.
All Starfleet starships are grouped by classes (design) and type (purpose). Unlike in the modern US Navy, the type does not necessarily refer to size (
Apollo is definitely bigger than
Intrepid) but rather to the type of mission the vessel was designed to carry out.
At least, that's my take on it.