What is the difference between 'rat' and 'mouse' in English? -.-
I have looked up and found a page that says the main difference is that a rat is bigger than a mouse.
It that is so, than in Chinese we do not distinguish between 'rat' and 'mouse'. We just call them 老鼠 or 耗子 (耗子 is more colloquial and dialectal). If you want, you can say 大老鼠 and 小老鼠 to describe them vaguely.
鼠 is seldom used alone. It is a morpheme that should be used together with other morphemes to form words, such as 老鼠, 田鼠, 袋鼠. These words cannot be abbreviated to 鼠. Maybe in scientific literature 鼠 can be used alone, but I think in that case they are more inclined to use precise terms in Binomial Nomenclature.
仓鼠 (hamster) is a common pet in China. Some other rodents are also common pets, but we do not usually call them 'X鼠'. For example, cavia porcellus (豚鼠) is usually called 荷兰猪, and chinchilladale (南美洲栗鼠) is usually called 龙猫.
The little white mice used in science laboratories are called 小白鼠.