UESPA Logo v3

well for me, it is like this. Basically UESPA has been around a lot  longer than the united earth gov't (est 2130). I feel that the name is too civilian and organizations like the later federation star fleet are quasi military. Basically UEPSA is like His/hers majesty naval service, which is the overall service that controls all of the United Kingdom maritime services. So UESPA has two organizations under its control: UESN (united earth stellar navy) and starfleet (officially united earth starfleet.) starfleet was founded in 2135. UESN was started in 2136. UESN is the military arm of UESPA and starfleet is for pure exploration. The UESN (which use naval ranks) was started when the united earth military(which includes the MACO), who official UESPA answers too but de facto was allowed to run its own show within bounds, realized the people in starfleet were too naive and could later cause problems for earth. So by the mid 2140's while starfleet had been doing some light exploration, UESN was patrolling earth and its colonys. Although it was ironic because by the mid 2150's even though the UESN was the military and starfleet was for pure exploration, starfleet had better ships than the military weapon wise even though the UESN was bigger. this happen when captain archer and starfleet revered its opinion on how starfleet handles weapons. well until the LC class. When the romulan war broke out, the UE military assumed more control of UESPA, UESN and starfleet. during the war they had to work together. while starfleet was fighting the major battles outside system, the UESN keep earth safe. starfleet had 3 fleets and so did UESN, although they were more the size of todays fleets (15-25 ships). when the federation was founded UESN and starfleet were merged and thats how Starfleet gots its, defense of the federation, secondary mission.  although the earth first fleet was formed with some old UESN as a navy under earth control. UESPA stayed in control of the earth based ships of starfleet and in control of the mostly earth, starfleet merchant marine and officially the first fleet, but those guys usually run their own affairs, until it mostly went away in 2300. A little complicated but hey I like it.

ships 

starfleet
Nx class
NV class (your Neptune class)
Nu class (your pioneer class) 1st class of ships
- neptune sub variant 
- gangs sub variant
daedalus class (older than NX)
Yorktown class
UESN
marshall
neptune (specs given to UESN for political reasons)
LC
Somerset

fleets 
1st UESN
2nd Starfleet
3rd Starfleet
4th UESN
5th Starfleet
6th UESN