Just a moment...
Some version of Macintosh software really will only want to work with files that have been recorded in the .MOV format. If you've recorded in AVCHD or .MP4 formats, you may have to Log & Transfer the footage, converting it into Apple's ProRes codec (or Apple Intermediate Codec) before your Mac will let you work with the footage.
Additionally, be aware that at least some versions of Apple's iMovie software simply won't work with 24P footage at all, of any type. There's no easy answer for that, other than to use different software to edit your 24P footage.
Regarding 4K or UHD footage, most modern Non-Linear Editing (NLE) programs should be able to work with the footage. If you're having issues, check with the manufacturer of your software — it's possible that you may need to upgrade to the latest version to be able to work with 4K or UHD footage.