Both refers to the two kinds of winds and seasons that occur in the country every year. Both seasonal rain and wind patterns that affects the Philippines.
Differences :
Amihan is known as the Northeast monsoon while Habagat is known as the Southwest monsoon.
Southwest monsoon bringing excessive rainfall and gusty winds to the Philippines from June to November.
Northeast Monsoon will bring cloudy skies with occasional to frequent heavy rains to the Philippines from October to March.