Dog and Cat are different words.

There are many word pairs in many languages that are written exactly the same way but have different pronunciations and different meanings.

You are thinking of the written language as the fundamental thing. Actually spoken language is fundamental, and writing is an imperfect representation of it.

The verb "lead" and the noun "lead" (i.e., the metal) are two different words, pronounced differently. The fact that they are spelled the same is just an example of how the English writing system doesn't encode the English language perfectly accurately.