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.
Filing the logo, and then the name
A design-only logo and the word it accompanies are different signs, and protecting one does not protect the other. The usual, and usually correct, answer is two applications: the word mark, which stops anyone using the name in any typography, and the design, which protects the specific graphic.
The word mark is the one people skip and the one that does the heavy lifting, because competitors rarely copy your exact artwork. They take the name.
Two more things to plan for. A logo that merely describes the goods, or that has become the ordinary way to refer to them, will be refused for lack of distinctiveness under article 173 of the Mexican Industrial Property Law. And when the logo is redrawn, the new version is a new application: registrations cover what was filed, not what the brand has drifted into since.