What is the word in majiang equivalent to suits in cards?
The measure word for 饼、条、万 is called 门, which literally means 'department; division; faction'. 

Example usage:


  ……序数牌……分“筒子/饼”、“索子/条”、“万子/万”三门，每门有序数从一至九的牌各四张。(from wikipedia)


An alternative measure word is (花)色, which literally means color/pattern. 色 is also widely used. 

When talking about the abstract concept of 'suit' in Mahjong, per my own experience 门 is more common, although 色 is perfectly fine too. There might be regional differences though.

When it comes to specific Mahjong terminologies like 清一色 or 一色三步高, those are set phrases in which 色 should not be replaced by 门.