Cadherins look like chains, that are stretched out only when bound to Ca++. They contribute to cell adhesion through adherens-junctions and desmosomes (cell-cell adhesion). They bind weakly by themselves, but function sort of like velcro, in that they make a strong junction when they are many.
Integrins can be of alpha and one beta type. Both types are used in a junction, and they sort of "claw" around the ECM. They also depent on Ca++ (and also Mg++) for correct binding. They join the cell to the extracellular matrix through aktin-linked cell-matrix juntions and hemidesmosomes. There's one alpha and one beta integrin per junction (i think) and they sort of "grip" the ECM by one of them going in the front and the other in the back of the ECM unit.
Both integrins and cadherins are transmembrane proteins, that also need adaptor proteins on the intracellular side.
Adherens junctions transfer the force of aktin filaments from one cell to another, using classical cadherins between the cells.
Desmosomes connect intermediate filaments between neighbouring cells.
Aktin-linked cell-matrix junctions link aktin filaments to the ECM.
Hemidesmosomes link intermediate filaments to the ECM.
Source: lectures at the university of Tromsø, Norway. Also my textbook.