What is the difference between the valence shell and the valence band? What is the difference between the valence shell and the valence band?
The valence band is usually defined as the highest filled band whereas Wikipedia defines the valence shell as the outermost shell of an atom in its uncombined state, which contains the electrons most likely to account for the nature of any reactions involving the atom and of the bonding interactions it has with other atoms.
This seems contradictory.
 A: Atoms in free space without interactions between them have a clear set of energy levels. Their electrons have certain energies that can be classified as shells. The lower energy levels are filled, while the highest one can be not completely filled. The highest shell is called the valence shell; these are the most interesting for chemical bonds and reactions.
If atoms are arranged in a crystal lattice, they are at very short distances from each other. The wave functions of the electrons overlap to some extent and there are a number of other interactions and disturbances (phonons, thermal variations, ...) that change the energy levels of each atom. In effect, this means that the valence band is not exactly at the same energy as for a free atom, but instead slightly higher or lower. Since there are on the order of $10^{23}$ atoms in a macroscopic crystal, there is a also consequently a large number of energy levels, all of which are very close together. This in effect looks and acts as a continuous energy band, not anymore as discrete, separate energy levels.
However, it is important to note that this doesn't mean that the valence shell is broadened and forms the conduction band, or that the shell below the valence shell broadens and becomes the valence band.
Instead, the valence shell and lower shell interact and form a new, hybrid shell. Each orbital in both shells is split in two, due to the Pauli exclusion principle. This combined band already contains $2N$ times as many states as a single, free atom has (where $N$ is the number of atoms in the lattice).
This combined band is further separated into two parts by interactions between atoms in the crystal, so that conduction and valence band appear. The valence band is the band that lies below the Fermi energy, while the conduction band lies above it. During the splitting of the individual energy levels in the shells, the some levels of the valence shell can be higher (lower) than the Fermi level, so that they end up in the conduction (valence) band.

The electrical properties of solids can easily be described with this band model, without considering the individual energy levels of each single atom. For example, the separation between the highest occupied and lowest unoccupied bands determines if the material is a insulator (large bandgap), semiconductor (small bandgap) or a conductor (no bandgap).
A: The valence shell is the outermost electron shell. An isolated atom's valence shell contain electrons with certain energy levels.
When atoms are brought into close proximity, repulsion of their electrons causes the energy levels corresponding to the shells to split into discrete energy bands. Thus the electrons will be separated by a short distance and have different energies within the band.
We consider the valence band in situations where the interatomic distance is short such as in crystalline structures. 

The valence band is usually defined as the highest filled band

The valence band isn't necessarily filled.
A: The wave functions of electrons in the valence shell of atoms results from an Hamiltonian, where the potential term comes from the Coulomb interactions. 
When two or more atoms are close enough, the wave functions of valence electrons changes, because the potential term has to include the Coulomb attraction of the other nucleus (and electrons). For the inner orbitals the change of potential is less relevant. 
Bonds are formed when the energy eingenvalues of the shared valence electrons are lower than the case of isolated atoms.
In the case of crystals, the periodic structure of the potential leads to wave functions called Bloch waves. They play the role of the valence orbital wave function of an isolated atom. While they are a product of a periodic function (with the periodicity of the crystal,  after all it is the source of the potential form) by a plane wave, we will focus in the plane wave part. A one-dimensional approach is the Kronig-Penney model, where band structures can be simulated. 
The lowest energy states correspond to wave lengths of the whole crystal. Then come the others until when it matches the atomic space. It is the same logic of quantized waves in a potential of a given length, and infinite energy boundaries. That completes the available states of the valence band.
For some metals, (ex: alkali metals) the valence orbital for one isolated atom has one electron, but it is possible to have another one of the opposite spin (to form an ion). They would have almost the same quantum number, except for the spin. 
It translates in the band configuration as one state per atom, but as two electrons of opposite spin can occupy the same state (the same position wave function, but differing by the spin) they will fill all the lowest states of the band using that "card". Half of the band, with the higher energy levels remains unoccupied.
They can easily migrate to adjacent levels in the case of an applied electric field, and these material have low resistivity.
The quantized wave lengths can also be shorter than one atomic distance. The largest wave length in this case must be a little shorter than that distance, in order to skip all lattice points except for the first and last one. The shorter of that type will have half the atomic distance as its wave length. That is the second band.
It is possible to simulate in the Kronig-Penney model that a gap may arise, depending on the potential function, separating that two bands. That is, an electron at the highest energy state of the lower band have no adjacent level to migrate. 
In that case, if the gap is large enough, and the valence band is completely full, (2 electrons for each band state), an electric field can't produce a current. The material is an isolator.
If the gap exists but is not so large, thermal energy of room temperature can move some electrons to the next band, according to Fermi-Dirac statistics. The few electrons in the upper band can now freely move, because have adjacent states available. That band is then called conduction band. The first band have also some available states now, and adjacent electrons can migrate to them. That states are called holes, and the band is the valence band. 
That are the semiconductors, and the amount of electrons in the conduction band (and holes in the valence band) can be greatly increased by the process of doping.
A: Within one electron description of the atomic states, valence electrons is an expression referring to the one-electron states which contribute significantly to  chemical bonds. Even though the most obvious shell to be considered as valence shell is the unfilled one, in many cases, it is necessary to take into account more than one shell in order to get a quantitative description of bond length and energies of molecules. For this reason from the point of view of atomic and molecular physics, valence shells is a generic name to denote the highest lying electronic states taking part to the formation of bonds. States at lower energies are usually referred as core states, and in many cases they can be treated as unperturbed by the chemical environment of an atom.
Going from atoms to solids, one could expect that this naming convention would be extended in such a way that valence band or bands would denote the band(s) of Bloch's  states originating from the one-electron valence states.
Indeed this is the approach used in the popular Ashcroft&Mermin textbook on Solid State Physics. In their Chapter 11, at the beginning of the section on "General features of valence bands wavefunctions" they clearly identify valence bands with the bands formed by the atomic states lying at energies higher than those of core states.
However, there is a footnote in the same page, where they notice that a different meaning is used for the same expression in the theory of semiconductors.
Indeed, at the beginning of Chapter 28 on Homogeneous semiconductors, they define valence band in a semiconductor the highest occupied band, according to the established use in semiconductor physics.
Therefore, the puzzling difference of definitions is actually due to real differences of naming conventions in different contexts. 
A: The conduction band is also formed from the Valence Shell Electrons. Using the same term "Valence" for isolated atom case and solid creates confusion.
