A warm front catching up to a cold front will ride up and over the tail end of the cold air.
This causes condensation in the warm front since it is reaching higher and colder altitudes.
The movement is relatively gradual, however, so widespread rain or snow results rather than abrupt storms.
This cold front moving in on a warm front forces the warm air mass to rise. Precipitation often results when this happens, because the warm air mass cools as it rises and cannot hold the moisture.