The Scots system is a mystery to me - and I currently have a teenaged offspring going through it
So, yes - there are the parallel English and Scottish courses, with exams in a bigger range of subjects taken at about the age of sixteen, give or take a year or so, and then exams in a narrower range taken either at seventeen (Scotland) or eighteen (England). This range of subjects is a matter of some choice, so the last compulsory music tuition happens at about fourteen - after this, pupils can opt out. Music learning as part of one of these academic subjects used to need supplementation with instrumental lessons to a reasonably high level - my understanding is that this aspect of musical learning has shifted focus somewhat.
The Scots have Standard Grades when the English are doing their GCSEs - but there's also a thing called Intermediate, and the thought, from what I understand, is that the former may be phased out at some point in favour of the slightly more demanding Intermediate level. The Scottish education websitey thing is about as clear as mud on all this though
. A year later than Standard Grades come Highers - in fewer subjects than Standard Grades, but with a broader sweep than A levels. Ambitious Scots will then stay on a further year and complete Advanced Highers or do a few A levels as well. It is possible to head straight up to university from Highers though - and this may be the reason why in Scottish universities the first degrees are four year courses instead of three as they are in England. As well as schools offering the various courses necessary to do these qualifications, people can apply to do them at later ages, through various further education colleges.
Separately from all of this comes the learning of musical instruments and for many, though not all, some theory to help with certain aspects of practical learning. Instrumental lessons are very often taken privately, out of school hours, but limited places exist within schools for kids to get tuition within school hours. This sometimes, but not always, involves taking the music pupil out of part of a standard school lesson, and is usually not that generously timed. Private lesson arrangements vary, but generally would have more time for the pupil. I think most schools in which there is a reasonable amount of instrumental tuition provided also try to run an orchestra. There is no across the board, routine, catch-all learning of instrumental playing in our schools. Kids doing music lessons, be that at school or privately, are often offered exams as a means of measuring progress, and this is where the exam boards come in. ABRSM is one, but there are others, notably Trinity Guildhall and the London College of Music: all set their own requirements for examination, but offer grades which are numbered in the same way and probably test to the same level for each grade: there's a bit of snobbism about that in the various camps though, with some thinking that their non-favoured boards are "dumbing down" the testing of musicians. Universities though will accept a grade 8 as grade 8, whatever the board. Grades can be taken by candidates of any age, so are also done by some adult learners, again as a way of measuring progress.
As well as this many towns run musical performance festivals, and have youth orchestra arrangements. The competition festivals can be used as a complement to the exam system, or indeed instead, with kids preparing music and performing it to small audiences with an adjudicator there. The winners in each class may then go on and perform in some sort of gala concert, depending on how the festival is run.