There’s no simplistic answer to what Preps do or don’t do, and the level kids are working at.
Some Preps are selective at 4+ or 7+ entry and have more able cohorts (even then there is a range) and many are not selective and have a range of abilities. They will mostly be set or grouped for Eng and Maths and the kids will be working at different levels and the curriculum being covered at different speeds. Some elements of Eng or Maths might be covered at a higher level to allow what state schools call ‘greater depth’ whilst others might not have been.
Preps are not confined by the National Curriculum, so some Maths techniques they don’t feel are as useful might be ignored and some of the grammar aspects of Eng might not be covered if they are seen as purely being for state school SATs which they won’t be doing.
In things like languages, they have often taught well beyond where state schools will be, having subject specialists and more time devoted to languages. But these don’t help students pass 11+. The other thing is huge sports provision meaning Prep kids often dominate sports teams when they get to senior level....although state kids who’ve played club sport can often be as good. Again, not useful for 11+, but parents pay for Prep school for more than 11+ and for a different schooling experience.
What they can do and will do is some 11+ exam prep, which state schools won’t. That will include some coverage or revision of curriculum topics, but vitally VR and NVR for many entrance exams. Preps which send kids to many different senior schools which include state grammars and independents are often prepping kids for a variety of styles of entrance exams. It can mean the prep isn’t that focused on particular skills and rather generic - which is why lots of Prep kids are also tutored by private tutors or parents too.
My kids are out the other end of it all now. Friends of mine, who were interested, educated and motivated parents sent their kids to a mix of private and state junior schools, with a view to selective seniors. The kids has different primary experiences but all got places at selective state or independent seniors. The state primary kids has some tutoring or parents did the work with them. Some of the Prep kids also had tutoring or parental work and some Prep kids just did what the school covered. They were all reasonably bright and that with the fact their parents were switched on and supported them, meant they got the places and we’re fine at senior level.
My kids went to Prep. They had a lovely experience, with a lot of running in the woods, heaps of sport and away matches, 3 languages including Latin, traditional teaching of English and Maths and a variety of brilliant and mediocre teaching. They entered senior school in a strong position and confident and positive. They had some maths tutoring outside school and I did some VR and NVR on top of what school did. If they had gone to the state school instead and had some tutoring and my input, I think they would have got into the senior school too.
Preps usually provide a different experience but they aren’t magically able to do something wildly different academically. They are a luxury, without a doubt. Bright kids from state schools who have interested parents who keep focused on how they are doing and who will put the time/money into prepping them themselves or using decent tutors (not so convinced about study centres with group work) have got a great chance.