As already pointed out, please make a new thread next time instead of necroposting.
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"Kuruma" is derived from "kuru" + "ma". "Kuru" is originally from an onomatopoeia of "something rotates/revolves/spins", and "ma" is an euphonic change of "wa", i.e.,
ring. Thus, it means "rotating ring". On the other hand, "uma" is derived from "ma", the pronunciation of the word "horse" in an old Chinese region. There is no relation at all between those words. Their pronunciations are just coincidentally partially close in the end.
"Kuruma" refers to the most common vehicle in the era, therefore it meant "gissha"
ox-drawn carriage in Heian/kamakura/Muromachi period, and "jinrikisha"
rickshaw in Meiji/Taishō period. It has nothing to do with horse, anyway.