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If "millimeter waves" have a wavelength of about 1 mm, one might linguistically expect microwaves to have a wavelength of about three orders of magnitude less, not the same or greater. How did microwaves get their name?
I did consider posting this on EL&U but think here it might get the benefit of more specialized knowledge or people more familiar with the concept of microwaves and wavelengths and the concepts being communicated by these terms.
The micro- in micro-waves, as far as I know, comes from the way that we produced electromagnetic waves at the time: following Hertz, people generally used currents cycling through antennas. Generally for broadcast the antennas would be huge affairs and would radiate in all directions. The radiated wavelength goes proportional to the antenna length because you want the antenna to resonate; so you got very long wavelengths. So, for example, according to Wikipedia, a 50m wavelength was used by Bowen's first antenna (the first radar antenna) in 1935.
Of course, microwaves existed before this point, with the first microwave generator usually credited to the Germans in 1920 (the Barkhausen-Kurz tube), and the online etymology dictionary listing a first usage of the term "micro-wave" to describe them in English from 1931. The OED expands on this with a quote that you can also read here, a 1931 article in the British Postmaster-General's "Telegraph and Telephone Journal", where they generated 18cm waves and reported immediate "undisguised surprise... that the problem of the micro-wave had been solved so soon." But the point was that at that time, it was very common to generate much longer wavelengths, maybe hundreds of meters long; it was not nearly so common to create smaller ones.
This terminology continued into World War II: more precisely, in 1940, a new device was created by John Randall and Harry Boot in the UK, called the "cavity magnetron." It was immediately applied to radar with positive results: it shrank the size of a radar antenna to the point where it could be mounted on an aircraft and used to detect a sub. At this point "microwave" seems to have been well-established usage for a wave which was much smaller than the large radio waves but larger than the infra-red opacity barrier of air.
Those cavity magnetrons became "microwave ovens" in the conventional sense, though the idea of using some sort of electromagnetic radiation to cook a steak was apparently demonstrated much earlier in 1931 in Berlin, with the chief innovation claimed there being a spiraling waveguide which transmitted the radiation through a ceramic pot into whatever wet objects were placed therein. These could well have been microwaves, given that in 1933 the above microwave tubes were old enough that they were being used by a German researcher to try to spot ships at sea.
