Correct, factor. Great Britain is the large island in which England, Scotland and Wales are situated. The British Isles is a geographical term for the two main islands (Great Britain and Ireland in its entirety) and about 5,000 smaller islands including the Isle of Man, the Isle of Wight, the Channel Islands and many far smaller islands.
Two sovereign nations occupy the British Isles - the United Kingdom and Ireland (the "South"). The Channel Islands and the Isle of Man form the three Crown Dependencies (as outlined in my earlier answer). They are part of the British Isles, but not of GB or the UK.
Great Britain is not a sovereign nation nor, strictly speaking, is it a geographical entitlty. I don't know the reason why IOM competitors take part for "Team GB"as they are neither part of Great Britain nor of the United Kingdom. I believe they do enter a team in their own right in the Commonwealth Games.