Types of trademarks include brand names (e.g. NIKE), slogans (e.g. JUST DO IT), and logos or designs (e.g. the Nike Swish symbol).
A logo and a brand name (or slogan) are two separate things in the world of trademarks, and they require two separate applications.
When you register your brand name (or slogan), it’s considered a “word mark” and what you’re protecting is just the name itself, completely separate from any font, coloring, or other styling. In other words, you’re preventing someone from using your name in their business, in any regard.
In contrast, when applying to protect a logo, the primary purpose is to protect the non-verbal elements from being copied by others. The registration for the Starbucks logo, for example, protects the idea of a mermaid inside a green circle, surrounded by stars and a block font.
Logo applications are important for unique designs that you wouldn’t want competitors to copy. However, if there is a budget for only one application, in most cases a word mark is probably a better choice as it provides the broadest possible protection of your brand name.