Metaphor and Simile

Metaphor and Simile are figures of speech. 

Metaphor is an implied comparison. In  a metaphor, there is no use of 'as' or 'like'.

Examples: 

Beware of him, he is a fox. ( It does not really mean that he is a fox. The sentence implies that he is a cunning person.)

She is a blooming rose. (This means that she is young and beautiful.)

A camel is the ship of the desert. (The sense is that as a ship carries people and goods at sea, a camel carries them in a desert.)

Simile is a stated comparison. In  a simile, 'as' or 'like' is used.

Examples: 

He is as good as gold. (His goodness is compared with the goodness of gold).

The matter is as clear as crystal. (The clarity of the matter is compared with the clarity of crystal).

The hoary head of his grandpa looks like a snow-capped peak of a mountain. (The appearance of his grandpa's head is being compared with the appearance of a snow- covered mountain peak.)