In Scotland, you automatically move up from your primary school to the associated high school - provided you live in the catchment.
If your child has an entitlement to be educated in a faith primary school, then the child automatically transfers to the associated faith high school (unless the parents have made other arrangements). Entrance to faith schools is slightly more complicated than entrance to non-denominational schools but straightforward for families known to the local priest (assuming it's a Catholic school).
In smaller regions there are sometimes only one or two state secondary faith schools, so most of their pupils are bussed in.
Schools have transition weeks before the summer holidays in order to facilitate the bedding in process. Placing requests are only required when you live outwith the catchment or when a whole-school transfer is agreed and only then would staff numbers and school accommodation be taken into consideration.
As all Scottish parents know, you also notify primary schools within a specific time frame of a new entrant to P1 or nursery, assuming you live in the catchment. There are only complications when it's a faith school or if a family lives in a rural area where the council is looking to close down a village school. Occasionally, there can be confusion because of a catchment boundary change or the construction of a replacement school, but - yes - the norm is for children to be enrolled in their nearest primary school and then to transition to the associated secondary.
During transition weeks, you'll sometimes see children who will actually be going to another high school (following a placing request) turning up at their associated high school with their primary classmates, but some primaries do keep those children at the primary for that week or organise for them to join in transition at their desired school if it's at all possible.
But yes - the norm is for children go to their nearest school, particularly at the primary stage. The catchment boundaries are sometimes more complicated in larger towns.