Huge difference here (Midlands) I can only compare the schools that my children have attended to this is by no means guaranteed to be the same across the country. I have 1 in Grammar school and had several through high school.
More GCSEs are taken around 10-12 instead of 7 (at this high school local to me) or 8. Latin and Mandarin Chinese are also offered in the Grammar. Just French is offered at High school.
The students are expected to go to University from the Grammar preferably a Russell Group Uni or Oxbridge instead of just being expected to get a few GCSE's and do anything upon leaving school as long as its not 'nothing'.
The extra curricular activities at Grammar are more like you would get at an independent school so things like rowing, combined cadet forces, archery, fencing.
School exchange trips appear to be to more unusual places so Iceland, Japan instead of the standard France or Germany.
I don't know any Grammar student who doesn't represent the school in some way. Either sport, music, STEM events, public speaking etc
Better access to national events at the Grammar. STEM/young engineers/Young Musician of the Year entries etc This does not happen at all at the local high school. There are no out of school activities other than football (boys team only) and netball (girls team only).
Enrichment is better at the Grammar. They expect more from the students at the Grammar. But bullying is more prevalent at the Grammar and less likely to be dealt with quickly. This is 1 area the local high school does better. Bullying is stamped out if they're alerted to the issue.
The Grammar school knows it has the top children and they expect them to achieve the top results. They expect the students to be driven and want success.
The High school just wants happy kids who do well if they can academically but who are offered alternative options if they're not able to pass GCSE's. They expect their students to try hard but it doesn't matter as much if they don't aspire to university. They don't have the facilities to offer the same opportunities as the Grammar school so they do what they can with what they have.