Archivist, antiquarian
A person who collects things can be called a collector. If the collecting is thought to be excessive, such a person might also be called a packrat, or a hoarder.
shoe collector or collector
A car collector?
A paper collector
A button collector??
a button collector
A badge collector.
A gem collector
A teddy bear collector! jk, i didn't know there was one. A person who collects teddy bears is called an Arctophile.
collecter
The proper term for that person would be known as a numismatist. There is no difference in titles between an American collector,a Canadian collector, or a European collector.
A numismatist studies the art and history of coins and coinage. Someone who just collects them is just a collector.