Why are certain things expressed as a matter of belief instead of a hunch?

Why are topics such as the existence of extra-terrestrial life, various monsters such as bigfoot and certain conspiracy theories spoken of as a matter of belief?

I can understand why someone could think ETs visited Earth, but why say “I believe” instead of “I think”? Are the terms equivalent in this context, or does the use of the word ‘believe’ indicate a stronger, less rational trust in the truth of the matter?