On Stagecoach East Kent's route listing all school routes are numbered 900+ and have school service listed alongside however I have anecdotal evidence that as they are service routes rather than private anyone can use them and also my Nan has used the school routes before
Therefore making it stupid to even call them school services in the sense that they are for students only
The difference, I think, is whether it is a registered service or a closed door contract. All of SEK's 900-series school routes are publicly registered routes, and anybody can use them. Arriva in the Medway Towns number all their school services in the 600-series. But as other posters have said, who would want to share a bus with a load of schoolchildren if they didn't have to? It is a service designed for schools, running at school times only, during school terms only. There is not going to be another one along in an hour, and the number helps make that abundantly clear!
Closed door contracts, by contrast, are strictly limited to school children attending the particular school, and most councils seem to use four-figure numbers or E-prefixed numbers. I'm not sure what the legalities of registration are, but others may know better.
Interestingly, when Herts CC used to produce books, they listed all of the E-prefix and "normal" services in the public timetables, just with a note on the E-series contracts restricting use. I would quote it, but my Herts books are too far down the pile for now.