There are seven broad types of logo, and each one communicates differently, connects differently and is protected differently.
The seven
Wordmark: the name in a distinctive typeface. Lettermark: initials. Monogram: interlocking letters. Emblem: text enclosed in a shape. Abstract symbol: a graphic with no letters. Mascot: an illustrated character. Combination mark: text plus graphic used together.
How the type changes your filing
In Mexico you can file a nominative mark (the words alone), an innominative mark (the graphic alone), or a mixed mark (both together).
A nominative registration is the strongest, because it protects the name in any typeface or colour. A mixed registration only protects that specific combination, so a competitor using your name in a different visual treatment may fall outside it.
The common mistake is filing only the mixed version because that is what the designer delivered. Then the company rebrands, the logo changes, and the registration no longer matches what is in the market.
What we usually recommend
File the wordmark first. Add the graphic separately if it is distinctive on its own and likely to outlive the current design. And remember that copyright in the logo belongs to whoever drew it until it is assigned to you in writing.