Your thumb points upwards, and your middle finger points to the right. In this world we can define vertices. These are just points that have 3 components that can each be projected onto these 3 axes. Vertices have no direction. Vectors on the other hand are by definition a direction.
Vectors are the difference of two vertices, hence they point from one to the other.
Vectors don't have a fixed origin, so they apply to any point in 3D space. You can of course represent a vector with a vertex, by assuming the second point in question is at the origin. So in essence, we only need one data structure to store both these types. Vertices are usually defined in world space. Which means they are in a predefined coordinate system, which you chose when you create your world.