At this point, Star Fleet (as opposed to Starfleet) more closely relates to the organization as seen in the Star Fleet Universe, as opposed to what has been shown on-screen since 1979.
(From a legal perspective, ADB are obliged to refer to "their" version as Star Fleet, based on the term as was used in the Technical Manual
; while the Paramount/CBS franchise has gone with Starfleet as one word instead.)
For what it's worth, ADB's Star Fleet (as detailed in works like Prime Directive Federation
) is primarily constituted as a star navy. However, that does not mean it doesn't have exploration as a major focus.
In peacetime, what usually happens is that, of the various numbered fleets (each with a particular region of Federation space to patrol), the Second Fleet is the one which gets all of the dedicated survey cruisers and other such ships, and is often considered to be the premier posting for those "who think survey duty is the highest calling". The ships of the Second are most commonly deployed in the coreward region not bordering one of the Federation's near neighbours, so has less of an overt need to engage in more "mundane" duties in their neck of the galactic woods.
That doesn't mean the other numbered fleets don't get to go on missions of exploration, but it does mean that issues like hunting pirates, patrolling border regions with rival empires, and other such military-minded operations are far more common than in the Second.
(The ADB-Federation was originally based on the "big Fed" map shown in the Star Fleet Technical Manual
, but was given further detail as more "native" empires were added, such as the Lyrans and Hydrans shown in the first two-and-a-half Starfleet Command
PC games. However, since it is a "big Fed" setting, that still leaves a lot of unexplored star systems within the boundaries of Federation space itself.)
None of this is directly relevant to what the Franchise has done with Starfleet post-1979, of course. But it does help show how some of the building blocks set in the Technical Manual
(many of which were discarded by Paramount/CBS themselves) have been expanded upon in another, semi-related universe.