The correct difference between a warm front and a cold front is best described by option B: In a warm front, the warm air gently rises above the cold air, and in a cold front the warm air is pushed quickly up.
Here's a brief explanation of the other options:
A. A warm front moves quickly, and a cold front moves slowly. - This is not accurate; typically, cold fronts move more quickly than warm fronts.
C. In a warm front, it is rainy and in a cold front it is clear. - While warm fronts can lead to steady rainfall, cold fronts are known to produce more intense and shorter-term precipitation, often associated with storms, rather than clear weather.
D. In a warm front, the warm weather pushes cold air up, and in a cold front the cold air pushes the warm air up. - This statement is somewhat misleading; cold air is denser and undercuts warm air in a cold front, forcing it to rise.
Thus, option B accurately represents the differences between a warm front and a cold front.