They mean pretty much the same thing but for some reason only 습하다 is used to describe the weather.

Thank you again ㅋㅋ

I forgot to include examples. ex) 요즘 날씨가 아주 습합니다. The weather is very humid these days. 오늘은 아주 습합니다. It's (very) humid Today. 한국의 여름은 매우 습합니다. Korea's summer is very humid.