Capstan versus turret
The term "capstan lathe" overlaps in sense with the term "turret lathe" to a large extent. In many times and places, it has been understood to be synonymous with "turret lathe". In other times and places it has been held in technical contradistinction to "turret lathe", with the difference being in whether the turret's slide is fixed to the bed (ram-type turret) or slides on the bed's ways (saddle-type turret). The difference in terminology is mostly a matter of United Kingdom and Commonwealthusage versus United States usage. American usage tends to call them all "turret lathes".
The word "capstan" could logically seem to refer to the turret itself, and to have been inspired by the nautical capstan. A lathe turret with tools mounted in it can very much resemble a nautical capstan full of handspikes. This interpretation would lead Americans to treat "capstan" as a synonym of "turret" and "capstan lathe" as a synonym of "turret lathe". However, the multi-spoked handles that the operator uses to advance the slide are also called capstans, and they themselves also resemble the nautical capstan.
No distinction between "turret lathe" and "capstan lathe" persists upon translation from English into other languages. Most translations involve the term "revolver", and serve to translate either of the English terms.
The words "turret" and "tower", the former being a diminutive of the latter, come ultimately from the Latin "turris", which means "tower", and the use of "turret" both to refer to lathe turrets and to refer to gun turrets seems certainly to have been inspired by its earlier connection to the turrets of fortified buildings and to siege towers. The history of the rook in chess is connected to the same history, with the French word for rook, tour, meaning "tower".
It is an interesting coincidence that the word "tour" in French can mean both "lathe" and "tower", with the first sense coming ultimately from Latin "tornus", "lathe", and the second sense coming ultimately from Latin "turris", "tower". "Tour revolver", "tour tourelle", and "tour tourelle revolver" are various ways to say "turret lathe" in French.
A subtype of horizontal turret lathe is the flat-turret lathe. Its turret is flat (and analogous to a rotary table), allowing the turret to pass beneath the part. Patented by James Hartness of Jones & Lamson, and first disseminated in the 1890s, it was developed to provide more rigidity via requiring less overhang in the tool setup, especially when the part is relatively long.
Hollow-hexagon turret lathes competed with flat-turret lathes by taking the conventional hexagon turret and making it hollow, allowing the part to pass into it during the cut, analogously to how the part would pass over the flat turret. In both cases, the main idea is to increase rigidity by allowing a relatively long part to be turned without the tool overhang that would be needed with a conventional turret, which is not flat or hollow.
The term "monitor lathe" formerly (1860s-1940s) referred to the class of small- to medium-sized manual turret lathes used on relatively small work. The name was inspired by the monitor-class warships, which the monitor lathe's turret resembled. Today, lathes of such appearance, such as the Hardinge DSM-59 and its many clones, are still common, but the name "monitor lathe" is no longer current in the industry.
Toolpost turrets and tailstock turrets
Turrets can be added to non-turret lathes (bench lathes, engine lathes, toolroom lathes, etc.) by mounting them on the toolpost, tailstock, or both. Often these turrets are not as large as a turret lathe's, and they usually do not offer the sliding and stopping that a turret lathe's turret does; but they do offer the ability to index through successive tool settings.