Some state schools can be a bit selective, I think. For instance, church schools (usually Catholic) are selective, in that they choose on the basis of your faith. But they still have to take some who aren't of their faith.
It does get confusing. Generally, there are state schools - which are usually comprehensive (the vast majority) or grammar (mainly Kent and a few other counties have them).
But, I know that there are some state schools which have exams and are selective, even though they're not grammar. I think they can take a certain percentage of 'high achievers'. Best to look at the details for each school.
Sorry it's not straight forward!