@Pitaramus As above, the SLT is literally management, like in any other organisation - those in charge (head, then deputy, SENCO etc if the school is large enough to warrant them) who make the decisions.
I think where you’re thinking of parents being involved that’s the governing body. This is comprised of staff, parents and other members of the community and has kind of an overseeing role, a check against the potential absolute power of SLT. They don’t tend to get involved in the day to day decisions, but instead take part in discussions about how budgets are spent etc.
All schools have SLT, but the levels of management depend on the size of a school (in primary). We’re a one form village primary, so it’s head, then part time deputy and SENCO, then teachers. In others you can have head, then full time deputies and leaders of KS1 and 2, then teachers.
All schools also have some form of governing body too.
The levels of management in all organisations, even schools, always makes me think of those human pyramids that cheerleaders make in the US 🤣