They used to be different countries. Until James VI of Scotland became the King (James I) of England as well. England, Scotland, Wales and Northern Ireland are states of the united country, "The United Kingdom of Great Britain and Northern Ireland". That's its official name, but people will say "UK", "GB", "Great Britain", or just "Britain" for short.
Personally I think they should combine them and dump the Jack, we haven't been a colony for 116 years so it's time to cut the apron strings. Didn't hurt Canada when they dropped the Jack in 1965.
Officially the UK's flag is called the Union Flag.
I think "Union Jack" comes from the Royal Navy, and refers to the short mast on which the colours are flown - and RN seamen have a proud tradition anyway of inventing nicknames for all manner of things aboard ship.