The Earth's tectonic plates constitute the lithosphere so no proper understanding of plate tectonics can be achieved without reference to the lithosphere, and this requires an understanding of its essential difference from the crust.
There are incorrect uses of both terms in text books - particularly common is the use of 'crustal', as opposed to 'lithospheric' plates - and these have contributed to widespread confusion and misunderstanding. The problem that teachers and, for that matter, authors of school text books have to face up to is that geologists need to employ two different concepts of layering within the outer part of the Earth to understand and explain geological processes - compositional layering (crust, mantle), and mechanical layering (lithosphere, asthenosphere).
What is the difference between the crust and lithosphere?
The crust (whether continental or oceanic) is the thin layer of distinctive chemical composition overlying the ultramafic upper mantle. The base of the crust is defined seismologically by the Mohorovicic discontinuity, or Moho. Oceanic and continental crust are formed by entirely different geological processes: the former is typically 6 - 7 km thick, the latter about 35 - 40 km.
The lithosphere is the rigid outer layer of the Earth required by plate tectonic theory. It differs from the underlying asthenosphere in terms of its mechanical (or rheological, ie, 'flow') properties rather than its chemical composition. Under the influence of the low-intensity, long-term stresses that drive plate tectonic motions, the lithosphere responds essentially as a rigid shell whilst the asthenosphere behaves as a highly viscous fluid.
The weaker mechanical properties of the asthenosphere are attributable to the fact that, within this part of the upper mantle, temperatures lie close to the melting temperature (with localised partial melting giving rise to magma generation). The base of the lithosphere is conventionally defined as the 1300 C isotherm since mantle rocks below this temperature are sufficiently cool to behave in a rigid manner.
The lithosphere includes the crust (whether continental or oceanic) and the uppermost part of the upper mantle. It thins to a few kilometres at ocean spreading centres, thickens to about 100 - 150 km under the older parts of ocean basins, and is up to 250 - 300 km thick under continental shield areas. Hence, whilst the crust is an integral part of the lithosphere, the lithosphere is mainly composed of mantle rocks. This is why authors sometimes state, loosely, that the lithosphere is the uppermost part of the mantle - they are choosing to disregard the thin veneer of crustal rocks.
Seismological evidence for the lithosphere and asthenosphere
The linear magnetic anomaly patterns in ocean basins were recognised in the early 1960s to be evidence for sea floor spreading and this paved the way for the development of plate tectonic theory, superseding the earlier theory of continental drift. The new theory clarified the requirement that there must be an outer rigid layer to the Earth (the lithosphere) decoupled from an underlying layer of lower strength (the asthenosphere).
The hypothesis that the Earth has an asthenosphere can be tested by searching experimentally for a layer with physical properties attributable to its low strength. Since the shear modulus of a material reduces as its melting temperature is approached the asthenosphere should retard the passage of earthquake S-waves, whose velocity is directly proportional to the shear modulus of the material through which it is travelling. The presence of a seismological low velocity layer (LVL) or zone (LVZ) near the top of the mantle thus provides evidence for the asthenosphere. The evidence is particularly convincing since S-waves, which are more sensitive to the prevailing shear modulus than P-waves, are slowed down to a greater extent than the latter. The low velocity zone is much better developed under ocean basins than under continental shield areas where it sometimes barely developed. Hence, oceanic lithosphere is much better defined seismologically than continental lithosphere.
Velocity-depth profiles through the Earth's upper mantle do not define the top and bottom of the zones of rigid and viscous behaviour precisely, however, because the zones must have transitional boundaries.