Both of them means eye, 眼 is a common word in our conversation while 目 is an old word in the ancient.

犬is a kind of written word. also is old chinese.狗is said commonly by people.

the first one is used in the articles writen in old chinese.the latter is commonly used now.but 目光，眼光 Are different.I think the use of the two words is depend on the situation you use.

no different talking chinese use 眼睛 没人会说"目"

目 is an ancient Chinese word of eye, 眼 is a modern Chinese word of eye, usually we say 眼睛， 眼 has another meaning, it means small hole.