Law school is where you do your Law degree...
Then you do either the Bar Professional Training Course if you want to become a barrister or the Legal Practice Course if you want to become a solicitor. These are at different private providers usually but some universities do provide the course usually newer universities although Sheffield University recently started doing these courses.
Then either you have found a training contract or pupillage and they paid for your BPTC or LPC and then they take you on for a training contract/pupillage in their company afterwards. Alternatively you have to pay for the BPTC or LPC yourself and then look for a training contract.
Post LLB (law degree) the legal professional training system is so ridiculously poorly thought through, exclusive and expensive. Awful profession.