An antiquarian is someone interested in antiquities, i.e. not just history but specifically historical objects. By contrast historians study the past through written texts.

Archaeologists study the past through material remains, so in a sense antiquarians can be thought of as amateur archaeologists. However, it's mostly a historical term; few people would describe themselves as antiquarians today. It carries the connotation of being interested in merely collecting artefacts and obsessing over physical minutiae, rather than using them to learn about the past.

In a nutshell: Historians are trying to ask questions about the past, using artifacts or evidence about the past. Antiquarians are collecting artifacts and evidence from the past, but for its own sake. Obviously a fuzzy line. But it's the difference between someone who is, say, trying to write a book making an argument about how technology played a role in the fighting of World War II, and somehow who is just trying to catalog every plane and tank used. Sometimes the products produced by the latter are very useful to the former, and vice versa! But they are pretty different relationships with the past, different kinds of work, and are usually done by different sorts of people working in different environments.