First let me state that just because throat glass or lower glass on a clock says "Regulator", that does not make it so.
The regulator was first introduced in the early 18th century when demand arose for a timepiece more accurate than the average domestic clock. Both astronomers and surveyors, whose observations required the utmost accuracy, needed regulators. These clocks were usually designed with a deadbeat escapement and were always weight driven. made exclusively to keep time, regulators omitted unessential complications such as striking mechanisms, calendar work, and moon dials. Furthermore, regulator movements were produced without motion works (wherein the hour and minute hands work off the same arbor) in an effort to reduce unnecessary friction. Therefore, instead of a typical clock dial, the dials of early regulators were sectioned into separate second, minute, and hour circles, each with its own hand.
During the mid 19th century, clock manufacturers produced high-grade wall and floor clocks that served as regulators. These clocks were found in public buildings, meeting houses, shops, and railroad stations where they were used to "regulate" other timepieces. Although these were still very accurate clocks, they often differed from true regulators or precision clocks insofar as they included motion works and traditional clock dials.
Over the years, the term "regulator" has been associated with many other styles of clocks. One of the best known examples is the Vienna Regulator, produced in Austria and Germany. These weight-driven wall clocks were usually very good timekeepers. At the height of mass production, clock manufacturers also introduced a variety of mass-produced "regulators" into the market. The most popular example is the Schoolhouse Regulator. These modest timekeepers were spring driven and lacking virtually all the characteristics of a traditional regulator or precision clock.
So what is a regulator? A regulator clock is a time only, with no additional friction adding features that is always weight driven with a verge/pendulum escapement that keeps extremely accurate time.