UTC: Universal time based on England.
GMT: Greenwich Mean Time. Sort of the same as UTC, based on a different region of the world.
Unix time: Number of seconds since epoch (1970). It is based on UTC. No timezones, there are leap seconds every now and then to adjust. They happen at the end of the day by just recounting the last second.
Computer systems should store Unix timestamps based on UTC.
Clients of those systems should do the adjustments to display them as local time to the users. At displaying time, a timeformat without offset is useless.