Stephen's answer is correct. I think you may be confused by the existence of the private school named Rugby which is named after the town of Rugby where it is sited. The game of Rugby was developed at this school and is named after it. The school Rugby is one of the oldest schools in the UK. It is what is termed a public school in the UK, the only requirement for attendance being ability to play the fees, at a time when other schools were restricted to the offspring of members of particular religious groups or trades. It predates state education in the UK, what would be termed public education in the USA. Rugby is an elite fee-paying boy's school.
There are no rugby "schools". Unless you mean schools that offer rugby as a sport that students can play. If you want to play rugby you join a club. You start at a "junior" club, in their lowest side. If you're any good you progress up the sides. You may even be good enough to join a "senior" club. Outstanding school boys might go straight to a senior club.
