There are two words for face or is there a slight difference?
顔【かお】 is the primary word for face (of animal/human). You should be using this word in most situations.
面 read as つら is an uncommon slangy/rough word that is mainly used in dirty conversations and derogatory idioms such as どの面下げて, 面の顔が厚い. Although some fixed phrases like しかめっ面 and 泣きっ面に蜂 are safe in ordinary conversations, you should not use 面 as a generic noun unless you intentionally want to offend someone.
面 read as おもて also means face or front, but this is a fairly literary and/or old word. You'll see this only in samurai dramas and stiff novels.
Standalone 面 read as めん (on-reading) is even rarer, and is used only in a few uncommon set phrases such as 面を通す. 面 read as めん also means mask (e.g. Noh mask) or surface. Of course 面 appears in many Sino-Japanese compounds such as 海面, 画面, 水面, etc.