What is pre-school?

[Tatat]

Is it associated with a particular school? So would I have to choose what school I wanted ds to go to in order to get him enrolled in that particular pre-school?

Or- DS goes to a nursery that takes them right up to school age and they have a room called "Pre-School" where the children are before they go to school full time.

Am I being a complete numbskull (actually that one doesn't really need answering thanks all the same )

Some are, some aren't. Most feed into particular schools though, so it can be a good way for them to make friends they will enter reception with. But if you are happy with the facilities I'd leave him there.
My ds went to a preschool associated with a primary I didn't want him to go to. He moved up to his current primary with only a couple of friends from pre-school and has already made lots of new friends, so I don't think that is really an issue.

Mine went ot a preschool, but it was a private nursery that had nothing to do with the local schools. For each of them there were about 4 children that went with them to their school

usually, attending a preschool at a link primary school does not guarentee admission into reception.
Preschool is the year before reception, so usually 3 and 4 year olds. My daughter attended for 2 years as her birthday is in September.

My DD goes to a community pre-school next to the infants school (but not connected iyswim). When my DS is old enough he'll go there if they can give me morning spaces but if they can only offer me afternoon spaces he'll go to the nursery round the corner instead. DD is currently doing afternoons and it is a PITA, would be more so if start working again.
My point is that a pre-school is just one option for spending your free 12.5 hrs of childcare for the 3+.