According to Wikipedia, "A full stop ( . ) (British, New Zealand and Australian English) or period (American English and Canadian English) is the punctuation mark commonly placed at the end of sentences."
"Full stop" and "period" are two names for the same thing, however it is used.
The colon is used to indicate that what follows it is an explanation or elaboration of what precedes it. That is, having introduced some topic in more general terms, you can use a colon and go on to explain that same topic in more specific terms. -- Larry Trask’s ‘Guide to Punctuation’.
Colons and semicolons are used to connect complete sentences, a colon to connect a specific sentence to a general sentence preceding it, and a semicolon otherwise. A period/full stop would work just as well as a semicolon, but a semicolon is normally used when the sentences are closely related. If they were connected with a conjunction you would use a comma.
Therefore, no: a colon is not a double stop. Probably the closest thing to a double stop would be a paragraph mark.
Now for a bit of history:
The full stop symbol derives from Aristophanes of Byzantium who invented the system of punctuation where the height of placement of a dot on the line determined its meaning. The high dot (˙) was called a "periodos" and indicated a finished thought or sentence, the middle dot (·) was called a "kolon" and indicated part of a complete thought, while the low dot (.) was called a "telia" and also indicated part of a complete thought. -- Wikipedia - Full Stop