A caliper is a device used to measure the distance between two opposite sides of an object.
Therefor under this definition doesn't a micrometer also count as a caliper?
As a result of numerous comments and some investigation I have rewritten my answer.
The Oxford English dictionary defines "caliper" as follows:
1 (calipers} An instrument for measuring external or internal dimensions, having two hinged legs resembling a pair of compasses and in-turned or out-turned points.
1.1 A measuring instrument having one linear component sliding along another, with two parallel jaws and a vernier scale.
Merriam Webster's dictionary has a slightly different definition for "caliper" and this is similar to the definition mentioned by @Dmckee:
Any of various measuring instruments having two usually adjustable arms, legs, or jaws used especially to measure diameter or thickness —usually used in plural a pair of calipers
"Micrometer screw" from the Oxford dictionary:
A screw of fine pitch attached to optical and other instruments for making fine adjustments of position.
Micrometer from Merriam Webster's dictionary:
1 An instrument used with a telescope or microscope for measuring minute distances
2 A caliper for making precise measurements that has a spindle moved by a finely threaded screw
The Wikipedia article "Micrometer" uses the term "micrometer-screw calipers" and notes that such devices were introduced to the mass market by the company Brown and Sharpe who were founded in Providence, Rhode Island.
The Oxford dictionary defines "micrometer" as follows:
A gauge which measures small distances or thicknesses between its two faces, one of which can be moved away from or towards the other by turning a screw with a fine thread.
It would seem to me that the term "micrometer screw gauge" is commonly used in the UK and "micrometer screw calipers" is commonly used in the US and any difference being masked by the usage of the shortened version "micrometer".
"England and America are two countries separated by the same language"
A micrometer is so named because it's for high-precision length measurements. There are several geometries:
The first of these is a type of caliper, since it grabs either side of the object you're interested in. The others, however, are for measuring interior lengths or depths, and "caliper" feels like the wrong word for those.