GMT and UTC are close enough that in casual use, treating them as identical won't get you into trouble. But there is a real technical distinction worth understanding.
GMT is a time zone; UTC is a standard
Greenwich Mean Time is historically defined as the mean solar time at the Royal Observatory in Greenwich, London — essentially, noon GMT is (on average) when the sun is at its highest point over that specific location. It's used as the UK's winter time zone (the UK switches to British Summer Time, UTC+1, in the warmer months).
UTC, by contrast, isn't tied to any physical location. It's a global standard maintained using a network of atomic clocks, adjusted occasionally with leap seconds to stay aligned with the Earth's actual rotation.
Do they ever show different times?
In practice, no — GMT and UTC are kept within a fraction of a second of one another, far too small a gap to matter in daily life. For virtually every practical purpose, from flight schedules to computer systems, treating "GMT" and "UTC" as interchangeable is perfectly fine.
Why UTC became the preferred technical term
As global telecommunications and computing grew, engineers needed a time reference that wasn't tied to a specific country's historical observatory and legal time zone rules (including its own Daylight Saving Time changes). UTC filled that role: a politically neutral, scientifically defined standard that every other time zone in the world is now expressed as an offset from.
The takeaway
Use "GMT" when referring to the UK's winter civil time zone, and "UTC" when you mean the underlying global standard — but don't worry too much if you mix them up in conversation. The numbers behind them match closely enough that almost nobody will notice.