I have often been consulted on elephant dilemas such as these. Mice are actually slightly bigger, and have more tusks than elephants. However a dead give away is that mice are usually seen smoking, whereas elephants rarely, if ever, partake in such vices. The only real difference is that:

'You get sugar mice, but there are no sugar elephants.'

As shown in a study by professor P.Dimbleby of Mouseology.

A cunning way to determine elephancy is to observe if, when in sight of brocolli, the questionable mouse/elephant runs to the brocolli trumpeting madly and proceeds to gobble the lot (Beware though, brocolli is a powerful aphrodisiac and elephants that eat too much may become unruly and prone to reckless behaviour).

Glad to be of assistance,

Dr. X (Elephant consultant)