beth (defunct)

I think there’s a shade of difference, perhaps just at the level of connotation: mecha has slightly stronger associations with anime & Japanese popular culture, while mech has a bit more of an occidental ring (perhaps in part thanks to the legacy of Mechwarrior). They’re used more or less as synonyms in English though, yeah.

(In Japanese, メカ, mecha, has a broader sense—any machine or mechanism—and the word narrowed in meaning when it was (re)borrowed into English. But such narrowings are common in loanwords, like what Japanese did with German Arbeit, which became not work-in-general but a part-time job.)