A cold front is the boundary between cool and warm air when the cool air is replacing the warm air. A warm front is the boundary when the warm air is winning the battle. When the pushing is a standoff, weather maps show the boundary as a stationary front. The stationary front is shown on a map with alternating triangles pointing away from the cold air and half circles pointing away from the warm air.
Color maps alternate the cold front blue and warm front red.
Frontal positions on weather maps show where the boundary touches the surface of the Earth. As shown in the graphic here, the boundary can be thousands of feet above the ground a couple of hundred miles away from the surface front. If there's enough humidity in the air, clouds and precipitation will form as warm air rides over cool air along a stationary front. Sometimes, stationary fronts can stay stationary or nearly so for days. When this happens, the sky can stay gray with rain or snow.