As far as I understand your question (which might not be much):
There are two different things that can exist here. For one, a cube has 8 of them. For the other, a cube has infinite of them (sort of).
A cube has 8 vertices. These are points (which we can think of as vectors, although some sources distinguish the two.) Yes, there are 8 of them, their locations are displayed to us as Cartesian coordinates, and faces and edges are created by connecting them.
When we render that cube, we get "infinite" samples. These are not actually generated from the object space of the cube, but from the positions of the vertices of the triangulated face that makes them. Think of a sample as being every single pixel that the cube takes up in screen space. (In reality, we're usually getting more than 1 sample per pixel.) So they're not actually infinite.
Although there are countless samples, we can still find things out about them. We know where they are in world, camera, or screen space. We can figure out where they are in any other space. We can figure out their UV. We know their normals.
Edges and faces are made out of the 8 vertices, and then the countless samples are made out of the 6 faces. When we do shader node operations, we are generally operating on samples, but true displacement operates only on vertices. Shader nodes work in parallel on all samples or vertices, so anything you do in a shader node will affect all samples and vertices using that material.
Mostly, there is only one kind of space, no matter how many vertices we have. The entire object exists in its own space, which can be converted to world space, or to camera space, or to the space of any other object. That space is integral to what we're doing-- it's how we know where the vertices are! The object space, and its orientation in world space, is necessary to know where to actually draw the faces/samples.
There is an exception to that, which is tangent space. There is a different tangent space for every single sample. If we displace along vertex normals, this is similar to tangent space in this regard, because every vertex has its own normal. We're still displacing in a single space, but if we start with a vector unique to every vertex (its normal), then multiply that by something constant, we still get something unique to every vertex.
If you add +1,0,0 to your UV, it will add that to the UV of every sample. If you add +1,0,0 to the vector given by displacement, it will add that to determination of bump for every sample, and/or will add it to true displacement of every vertex.
A sphere has more than 8 vertices, but it certainly doesn't have infinite vertices; a default UV sphere has 482 vertices. If you do true displacement on it, you will do true displacement on 482 verts instead of 8. It has no more or fewer samples than a cube, because the number of samples has nothing to with shape.
