Yeah, important point. There are four closely-related CG terms buzzing here: - Vertex: A point, a dot, a location in space described by (X,Y,Z) coordinates. You can’t “see” it, therefore the notion of “materials” or “textures” makes no sense. - Edge: A line, drawn between two vertices (“points”). The edge itself has no width, no height, only a length. Once again you can’t see it, and so it has no “material” or “texture.” - Face: A triangle, square, or other polygon (“n-sided figure”) which is defined by three or more edges (“lines”). All of the edges must be on the same plane; that is to say, the face is flat. You can see a face, unless it’s edge-wise to you. It has a material, textures and so-on. - Materials and textures: These tell Blender how the different faces of an object should look. Each object can have one or more materials assigned to it, and each face contains a “material index” which selects the particular one of the object’s materials that should be used to draw this face. (Each one of an object’s materials can have one or more textures assigned to it.) So that is how you can create a cube with red faces and blue ones. It’s also one way you can create a pair of gambling dice.
A face is recognized by the vertices (“points”) which define its boundaries. The same is true of each edge (“line”). When you select both of the vertices that define an edge, the edge turns yellow. If “Draw Faces” is on, when you select all of the edges which define a face, the face turns pink.
Edit mode is a “vertex-oriented” tool, so each mouse click is associated with a particular vertex. Meanwhile, UV Face Select is a “face-oriented” mode, so each mouse click is interpreted as a reference to an entire face; therefore necessarily including all of the edges and vertices associated with that face. (And Object mode is … guess what. Exactly!) If you switch from one mode to another, which you can do at any time, you’ll see that their actions always remain consistent with one another.