A cold front is when the boundary of an advancing mass of cold air (high-pressure system) and the warm air (low-pressure system) meet but don't crossover and the cold air pushes and forces the warm air up. A cold front is defined as the transition zone. Cold fronts generally move from northwest to southeast.
A warm front is a boundary of a cold mass and a warm mass and the warm mass replaces the cold air mass. A warm front is also defined as the transition zone. Warm fronts generally move from southwest to northeast.