I agree with the above, that traditional quill stems, that have a horizontal* extension when installed, are measured center to center on the horizontal plane.

*These typically have a 17° angle between quill and extension, and so ideally fit a bike with a 73° head tube.

The problem with that, however, is that for the last 30 years or so they've been making stems with a variety of angles, which are not always indicated in a uniform manner (a stem with a 90° angle is sometimes called a 90° stem, sometimes 0° rise). Add to this the phenomenon of threadless stems that can go either easy, +10° or -10°, and so on, things can get very confusing.

When I measure a stem now, I measure it as if it had a 90° angle. That is, a dimension perpendicular to the steerer, measured center to center; this is the length of the stem, and it is a property of the stem. At the same time, I measure stem height, which is a property of the setup of the bike, since it is variable.