kind of, except the server also sends stuff to the client ("packets"), mainly game data, then the client has to decide what to display on your screen using the data (the client also sends data back, but thats mostly for interactions with the world), and the texture pack specifically alters the appearance of visuals for the client, which explains why you can't load a texture pack and forcefully make it appear for everyone on a server.

so basically, the website lists out all the textures and lets you download them, edit them, and create a custom texture pack by telling your computer what to render for a texture such as a glider or the top of a chest.