What are the differences between active transport and passive diffusion?

The main difference is that passive diffusion DOES NOT use up any ATP, while active transport uses up ATP with the Help of channels that are selective to particular substances.

Only simple substances can pass through the cell membrane in passive diffusion, therefore the transport of ions and other bigger molecules would have to be handled by the ATP channels and must undergo active transport to enter the cell.

active transport requires energy usually from ATP and transport proteins, in pasive difussion the elements go through the membrane because they have similar caractetistics in favour of a concentration gradient, it doesn`t require ATP

Diffusion occurs because of concentration gradients.  All molecules have a tendency to move from areas of high concentration to areas of low concentration - for example, the sugar you put in your coffee or tea spreads out until the whole cup tastes sweet.  Diffusion does not require any energy,  but it not usually considered a membrane function.  Many things - water, and any ions, for example - cannot move directly through a membrane, because they are polar.  Only things that are hydrophobic can move directly through the membrane.  However, the membrane does have specialized structures - transmembrane proteins, many of which form pores or channels.  Some are open all the time, while some are gated, and water and ions can move through these aqueous pores.  
    Active transport is different.  It requires energy (usually ATP) and often moves things AGAINST the concentration gradient.  An example is the Na/K/ATPase.  It moves Na out of the cell and K into it (in both cases from an area of low concentration to an area of high concentration) using the energy from the break down of ATP.

Passive transport:
- involves carriers, channels, or direct diffusion through a membrane.
- always operates from regions of greater concentration to regions of lesser concentration.  
- No external source of energy is required.

Active transport:
- directly uses ATP (for Primary Active Transport)
- possible to go against the concentration gradient.
- a source of energy is required to move the carrier and its materials.