Do MO's span a bond or the whole molecule?
The unfortunate answer is: both, and it is rather complicated. It can be noted at this point, however, that between two atoms connected by covalent (or even ionic bond) there are MOs.

Molecular Orbitals, the Wave Function, and the (Electron) Density

In quantum chemistry, we can define:


(spin) MO: a one-electron wave-function. Contains one electron, can be combined to with another spin MO to form what we usually think of as an MO, that is, doubly occupied.
Wave Function (WF): Typically a product of MOs, at least in the simpler approaches (Hartree-Fock [HF], common Density Functional Theory). The product is anti-symmetrized such that it obeys the Pauli principle. These products of MOs can be linearly combined to yield more accurate, complicated and expensive approaches.
Density: The expectation value of a WF when applying the density operator. Out of the three, this is the only true observable, for instance by X-ray diffraction. If you have a open shell molecule, you may be able to observe a spin-density, for instance by Electron Spin Resonance spectroscopy.


What's the point of these definitions?

They illustrate that a MO and the observable density have a few steps in between. Let's assume that someone gives us a set of MOs which yield the correct density of a molecule (as well as other correct observables). This is already a tall order, by the way. It is a mathematical fact that one can "rotate" the MOs, that is, create new MOs from linear combinations of old ones and still yield the correct density. So the set of "correct" MOs is not unique by the reasonable measure that it should give us the correct density.

OK, so there is more than one set of "correct" MOs. So what?

For one molecule/method/basis set combination, many ways of "choosing" your MOs are possible and lead to very different pictures, even when choosing reasonable contour values (say, 85%) for the visualization. An incomplete list is:


canonical MOs: these are eigenfunctions of the Fock operator, which is central to HF, but also of relevance for post-HF methods. They also preserve meaningful orbital energies (which relate to ionization potentials), but they are usually completely delocalized over the whole molecule.
localized MOs: "rotations" of the MOs have been performed to yield orbitals of (hopefully) minimal spatial extent. They are more easily interpreted, but the mathematics involved is iterative, meaning that minor changes in molecular geometry could lead to rather different local MOs. There is also more than one scheme to do this, and the results can be fairly different.
natural MOs: suppose you have performed the very accurate/very expensive calculation of full Configuration Interaction (full CI) for your molecule. The resulting orbitals are then eigenfunctions of the true Hamiltonian (in the given basis set). You will probably never encounter these due to the sheer cost of the calculation - and they may not look all that different from canonical orbitals.


And then there is the small issue of virtual/unoccupied orbitals

They do not enter the density (duh), but are often relevant to discussions of mechanisms, such as initial point of attack or stabilization. In my opinion, there is basically no way to pick a good scheme for them - canonical orbitals sort-of yield electron affinities.

Then all hope is lost. There's no way to choose.

Well, for occupied orbitals, there kinda is. One should compare orbitals (of one computational level) with each other across molecules to get to useful results. The textbooks usually do not give you this opportunity because you have no idea where those orbitals come from.

Back to OP's question: yes, canonical orbitals would extend over basically the whole molecule. You are being shown, in all likelyhood, orbitals that have been localized somehow. They are used as illustrations by the authors and that's usually not a bad idea. Take 'em with a grain of salt.