In Canada (probably also in USA), anyone who creates a written work or piece or art / design automatically has the right to control its use and distribution - in other workds, the creator has an automatic copyright. However, establishing who was the creator and when that was done legally can be troublesome. That's what the fee thing is for. You can take a copy of your creation to a government office and deposit it with them for a fee, receiving in return a document showing the exact date and time the copyright was registered. That still does not settle who was the creator, it only establishes a time at which that particular version of the work existed.
Trademarks are different. They are words and / or designs that are used as unique identifiers in commercial trade. As such they must be sufficiently different from any existing trademark that they cannot cause a consumer to be confused about the items' identity. But this also take into account the field of use. Suppose you trademarked the name "Shuv-El" (I know its bad!) for a device you could temporarily fasten on the front of your car to push a friend's stalled vehicle. Then someone wants to trademark "Shuv-Ul" for some new design of a garden spade that claims to reduce back strain. Sure the names are extremely similar, but nobody would confuse the two devices because of their vastly different designs, markets and uses, so it's possible both could be trademarked. But because of the somewhat "fuzzy" ways Trademarks can be used, and because they are important in generating income, a central (read, government-operated) registry of Trademarks is necessary so they can be searched and compared.
chusteczka raised a good point: these are matters of civil law, and enforcement (including detection of possible violations of rights) is entirely up to the holder of the rights. There are no Trademark Police or courts to do it for you.