Record
REC records everything received on the channel to Download/DMR/Audio. Play them from Last heard → Recordings.
Monitor
MON tells the radio to pass every digital call it can decode on the channel, not only those addressed to you or to the talkgroups in the channel's list. On the firmware the phone shipped with, that is the radio's own monitor mode. With the bench firmware FW26 or later, MON also sets the module's promiscuous flag: every call on the channel is admitted whatever its talkgroup, ID or colour code, and each call's colour code and time slot are shown on the caller line and in history (CC 1 TS 2). It is for the current channel: changing channel (arrows, scan, zone, the car) switches MON off, as the radio does, and the button goes dark.