in "1940 Wadoryu Karatejutsu was registered at Butokukai, Kyoto for the demonstration of various Budo, together with Shotokanryu, Shitoryu and Gojuryu. This occasion is regarded as the first official naming of Karate styles."
This is a quote from
http://www.hogia.net/karate/karate/history.htm
I think this is where the four come from. Three out off these four styles had Okinawan teachers that introduced the style to mainland Japan, wado-ryu has a Japanese founder.
So "the four" are the first four historically in japan, i.mo.. Kyokushin comes from shotokan and goju-ryu I believe.
Although some karate was formed into a style in Okinawa (goju-ryu comes to mind) other karate was this or that teachers karate (or whatever term used then). I believe I've heard it said/written that Funakoshi never claimed a particular style he said he taught karate. I think much off the organisation into ryu's (schools) is a japanese thing.
Ryushikan: Above linked site and
http://www.wadoryu.org.uk/ provide good history on Ohstuka sensei i.m.o.
hope this helps,