Classical Theory - (proponent: Adam Smith) Wages and prices are flexible. The economy self-adjusts to deviations from its long term growth trend. Minimum government intervention is required. Persistent unemployment requires supply side policies e.g. deregulation and tax cuts.
Classical Equilibrium - Short run equilibrium occurs where the short-run aggregate supply curve (SKAS) intersects aggregate demand (AD). This is temporary. The economy will self-adjust so that both curves will intersect on the Long-Run Aggregate Supply (LRAS) thus achieving economic stability with full employment.
Keynesian Theory - (proponent: John Maynard Keynes) Wages and prices are slow to change. Private demand is inherently unstable, thus requiring active government intervention. Persistent unemployment requires demand side policies, e.g. increases government spending and tax cuts.
For a review of these theories, go to the MIT Open Course on Macroeconomics