^With the fugitive, it is a similar situation as with Kirk & co. Vulcan gets special treatment in the Federation.
But you should also note the wording: they don't say civilian or something, but Vulcan.
Here is my personal view that will probably go against Christopher's newest book, but once I reed it, I will try to adapt:
The form of Starfleet is not set in stone, as did the actual system of the Federation change over the centuries (from alliance, trough confederation to the present federation, after all, with a low number of members many features were not required) so did Starfleet.
Generally we equate United Earth Starfleet with the Federation Starfleet. But we should not that the Federation Starfleet also contains vessels of some other members (founders for sure, and also some that were somewhat significant before joining).
Lets take a look at the early Starfleet:
The main shipbuilding is in the hands of humans, the have the biggest fleet (as the other 3 members were decimated in the Earth-Romulan war) and they are eager to boldly go...
It would take a decade(s) before the Vulcan, Tellarite, Andorian fleets are at their pre-war levels, if they are rebuilt at all (the Vulcans' new isolationism would not push them to rebuild their fleet).
By TOS, Earth Starfleet dominates the Federation Starfleet. At that time new members join Starfleet rather then build their own, some like never built them in the first place.
(I felt that the conflict Starfleet Academy vs Vulcan Science Academy was a racial one, rather then in academic quality, so it would point to a separation between Starfleet and a Vulcan force. But both would still exist under an Federation Starfleet umbrella...)
But back to actual numbers, here are my guesstimate (ENT from screen and novels, TOS-TNG from registry numbers):
United Earth Starfleet, 2155: 90
United Earth Starfleet, during TOS: 1039 (972-1106)
United Earth Starfleet, 2293: 1114 (961-1267)
Federation Starfleet, 2373: 28883 (28247-29519)