The full title of this state is The United Kingdom of Great Britain and Northern Ireland. Great Britain consists of England (population 55.3 million), Scotland (population 5.5 million) and Wales (population 3.2 million). The 'Great' in Great Britain is nothing to do with being wonderful, it is a geographical term to indicate that all the lands and islands of Britain are included.
Northern Ireland (population 1.9 million) is not part of Great Britain. It is part of the United Kingdom however which is why it is included in the full title.
The UK flag is correctly called the Union Flag. It is often referred to as the Union Jack although it is only a Jack when flown on the jackstaff of a ship. This might be the origin of the nickname; another theory is that it refers to King James VI of Scotland who in 1603 also became King James I of England, thus bringing the two countries under one crown for the first time.
The Union flag combines the flags of England and Scotland with the later addition of the diagonal red saltire or offset cross to represent Ireland. This offset is important as the saltire cross does not sit centrally in the white of the St Andrew's Cross of Scotland. This means there is a right way up and a wrong way up for the Union Flag. Few people realise this. Flying the flag upside down is considered offensive by some but it has also been used as a subtle distress signal in the past recognised by British observers but unnoticed by the enemy. What about Wales? The Welsh flag of a red dragon on a green and white background does not form part of the Union Flag. The reason is that while England, Scotland and Ireland were Kingdoms, Wales was of lesser status as a Principality.
The easy way to recognise if the flag is the correct way up is to look at the broad white area of St Andrew's Cross which next to the mast should be uppermost. If the flag is displayed without a mast, it is assumed the mast would be to the left.
The left image is correct.