What is the difference between, "The book was very boring and it belonged in a dustbin" and "The uniform looks like it belonged to a museum collection".
Belong to is generally possessive:
Belong in (or on or_under_, etc) indicates that something should be in (or on, or under) a certain position:
In case of the museum collection, actually both are possible, but they have a different meaning:
It looks like there is a museum that has this uniform in its collection. The uniform looks like it was removed from that collection.
This uniform may not literally be taken from a museum, but it should be in a museum.
Another example to show the difference:
The car may have been stolen from John.
I think John should buy that car. It fits with the rest of his collection.