Demand for money 

The demand for money is a more difficult concept than the demand for goods and services.  It refers to the desire to hold one's assets as money rather than as income-earning assets (or stocks).

Holding money therefore involves a loss of the interest it might otherwise have earned.  There are two schools of thought to explain the demand for money, namely the Keynesian Theory and the Monetarist Theory.

The demand for money and saving

The demand for money and saving are quite different things.  Saving is simply that part of income which is not spent.  It adds to a person's wealth.  Liquidity preference is concerned with the form in which that wealth is held.  The motives for liquidity preference explain why there is desire to hold some wealth in the form of cash rather than in goods affording utility or in securities.