Mices and rats: differences between shǔ, lǎo shǔ, Xiǎo lǎo shǔ, etc
In most conditions, Chinese Mandarin doesn't divide "rat" and "mouse", but 鼠 and 老鼠 can mean different creatures. 鼠 means various of mouse-like creatures, like voles, hamsters, guinea pigs and so on, while 老鼠 only means rat, that grey little creature. 

Hope it helps, I learned these from an online lesson I was taking, it's the ECL(eChineseLearning), they have got a free trial, and basically that's why I enroll their classes. Just for your consideration if you want to learn Chinese systematically, visit at http://www.echineselearning.com/free-trial/ for a free trial.