For years the common unit of measurement in typesetting was the em. As the name implies it comes from the letter “m”, the widest in the alphabet. Allegedly, whether the font is large or small, the average over the line, page, book, will be 2.5 to 3 characters per em. (I haven’t checked this assertion.) We used to use “em” when we meant 12pt em, but that was strictly speaking incorrect: this pica em was often used as a quick and dirty standard measure. An em space will actually be as wide as the type size in question. An en space is half that size. Thus if the font being used is 10pt, the em space will measure 10pts by 10pts. This doesn’t have to mean though that you can just measure the width of the printed letter “m” and discover the font size. Although it gets its name from there, the em doesn’t have any real relationship with the image. There must have been type founders back then who did make an “m” which was as wide as the font size, but this is no longer an absolute rule.
Printers like to be able to measure precisely. Hart’s Rules tells us that Oxford University press used a 96-unit system. Using this system you can see the relationship between the various spaces — though this has nothing to do with font size. Whatever size the type, the em will still be divisible by 96.
Em quad space = 96 units
En quad space = 48 units
Thick space = 32 units
Middle space = 24 units
Thin space = 19 units
One point space = 8 units
Half point space = 4 units
Quarter point space = 2 units
Just to keep confusion levels well elevated, I should point out that you cannot assume that OUP’s one point space will measure 1 point. Unless that is, you are setting 12 point type. The one point space is 1/12th of the em quad; thus with a 12 point font, you will have a one point space measuring 1 point. If you are using 9pt type, the one point space will actually measure 3/4 of a point, with 6pt type, 1/2 of a point, and so on. Furthermore, the point size of the font cannot be measured by any bit of its printed manifestation, since the type size is the size of the body, not any of the characters. This handy picture shows with its red bracket the measurement which would yield the type size.
Of course this is all stuff which the passage of time has taken care of: we don’t get our books set in hot metal type any more (unless we are in the de luxe business). These physical things which had to be combined into a row of tiny metal objects to create a line of type exactly the same length as the ones above and below it, have all been replaced by a rather simple calculation by a computer. You will also find direction all over the place telling you that you can measure font size by measuring the type on the page: they’ll say it’s the distance from the top of the ascender to the bottom of the descender. Maybe on your computer that’s even true: there has to come a point when if everybody says “x”, “x” becomes true. Insisting on talking in terms of an obsolete technology is just dumb, unless, I guess, you are talking to other technologists.