Prety much the same.
Perhaps be prepared for more homework. Also will your child now have separate subject teachers. And expect end of year exams. All of which will add up to the need to pick up study and organisational skills. (Having them in place is an advantage for secondary though.)
Expect some catch up in French or Latin, and even maths and English. (More essay writing.)
I would be inclined to be a bit more hands on in the first few weeks in terms of overseeing homework and helping learn for tests. If it an academic school leading to say Common Entrance, and might prove a big jump you might go and see the Head of Year to see if there is anything you might go through in advance, eg what they have been covering in science to ease the transition.
I suspect that you are allowed to demand more time off form teachers in the private sector, so at the start do just that .
If your child is sporty or musical it might be worth a word. Sports teams, choirs etc will be established, but extra curricular is one of the strengths of the private sector and a way of getting to know other children, so talk to the form teacher about how your child might get involved.
Do try to go to parents things, as this helps for future playdates. You may find an organised PTA will be helpful and welcoming, but again cliques may have formed. Just grin and bear it and try to spot others sitting on the sidelines.
Many schools provide a list of pupils with their addresses. See if the school secretary will give you one in advance so you can have a couple of play dates and maybe even find some school run shares.
Does the school allow a taster day in advance of starting? Or are there any events, such as fetes, that you could go along to.
I hope I have not made it sound as if there is anything to worry about. There wont be. Children adapt quickly and the school will know what they are doing.