My experiences are similar to those already posted to this thread, but I've also encountered some differences that may be of interest.

Some state historic preservation offices have drawn a pretty hard line between architectural history and archaeology.  They allow recordation of standing structures only by a person holding a degree in architectural history and they are fine with the fact that such records often overlook other site elements such as cellars, wells, paddocks, and stack yards (for example); presence of archaeological elements does not require an archaeologist.  A person holding a degree in anthropology/archaeology can record archaeological sites and when those contain standing structures they have to bring in an AH.

Some states allow an archaeologist to record standing structures provided they can do so with the correct terminology and emphasis.  These data may or may not be submitted on the archaeological site form, depending on the state's standards (some want standing structures also reported on a structures form).

By the way, until about 5 years ago one of the states in which I've worked reserved the trinomial site numbers for prehistoric archaeological sites only.  Historic archaeological sites were assigned some other identifier and had to be recorded separately from a prehistoric site even if both components were in the same space.  Historic structures were numbered in a third and separate system.