Similarities:
Both involve ion movement. Both use ion channels to move ions across the cell membrane, in or out of the cell.
Differences:
Passive Transport (or Diffusion) moves ions from high concentration to low, using no metabolic energy. Active Transport moves ions from low concentration to high, using metabolic energy in the form of ATP. Active Transport uses an ion pump (or Sodium/Potassium pump) to move 3 sodium ions out of the cell and 2 potassium ions in to the cell through the energy of 1 ATP molecule.