1.Partial equilibrium is a condition of equilibrium in the theory of economics which takes into consideration only a part of the market to attain the equilibrium. It studies the effect of one variable upon the other without considering the effect of other factors.
For example, law of demand is studied in relationship with price by keeping all other factors constant.
2.General equilibrium is the equilibrium that studies an economic phenomenon by taking all the aggregate units in the economy into consideration.
For example, product prices make demand for each commodity equal to its supply and factor prices make the demand for each factor equal to its supply so that all product markets and factor markets are simultaneously in equilibrium.