Both copyright and trademarks protect intellectual property. However, whilst copyright protects original works of art, such as music or literature, trademarks typically protect brand names, logos, and slogans.
In simple terms, copyright is the right of the owner to make copies and typically protects something that the company produces. A trademark protects the brand's identity (or really the brand itself) from infringement. A trademark protects something that identifies the company and distinguishes it from other companies in a given market.
A brand logo can be both trademarked and copyrighted. It is not uncommon to both copyright and trademark your logo, as a trademark might offer a limited scope of protection.
Generally, a trademark must be connected to certain goods and services sold under the brand logo. Copyright, on the other hand, applies to the original work of art in nearly any instance of its use. However, to be able to copyright your logo, it must be original.
You can read more about the various IP protection mechanisms in our article Trademarks, copyrights, designs & patents.