A trademark identifies a business in the marketplace. It can be a word, a logo or a combination. You file it in a class of goods or services. After registration you may use ®. Before that, ™ is a claim, not a certificate.
Copyright protects an original expression — the text, the illustration, the software code, the film. It exists on creation. Registration is evidence. A logo can be a trademark when used as a brand and an artistic work for copyright. Many brands file both, for different reasons.
A patent is a third thing: a technical invention. A design registration is a fourth: the look of an article. Calling all of them ‘patent my logo’ is how applications get filed in the wrong office.
If a mark is already in the Trade Marks Journal or on the register, filing an identical name in the same class wastes the fee. A knock-out search is cheaper than an objection reply.