Hugh, if you're trying to understand the distinction between vector and raster mapping, then I'd suggest thinking of vector mapping as a description of a picture, and raster as an actual picture constructed from a set of dots.
Vector descriptions can be interpreted by some tool, to create a picture, or for all sorts of other reasons. Essentially, a vector description is, as you say, a collection of numerical values, and some means of identifying what those numbers represent. In the simplest vector notation, each element would be simply a line between two points, in 2 or 3 dimensional space. More sophisticated vector notations could include complex shapes such as arcs, circles or curves, etc.
Many of the graphics formats use vector notation, such as PostScript or SVG.
Given a vector notation, you need a rendering engine to convert the notation to a picture that can be displayed or printed. Now, whilst some of the earliest computer graphics terminals used vector displays, almost all are now raster-based; that includes laser and inkjet printers and televisions.
The OS might use a bespoke geographical information system (GIS) to enter and manipulate mapping data, but at some point they'll need a rendering engine, with rules to determine how features are drawn. This may be bespoke, too, or it may be one of the various GIS systems available. Even then, I bet there's still a lot of human manipulation of the various 'layers' of information that are drawn on a map; where place names are put, for instance.
In rendering a map at different scales, different amounts of detail will be used; e.g. a 1:10k will show more 'crinkles' than a 1:50k map. There are various techniques for 'point thinning', or simplifying lines, and you might be familiar with them from GPX import functions of mapping tools such as WheresThePath.
