  The microcanonical ensemble is in important physical situations different
from the canonical one even in the thermodynamic limit. In contrast to the
canonical ensemble it does not suppress spatially inhomogeneous configurations
like phase separations. It is shown how phase transitions of first order can be
defined and classified unambiguously for finite systems without the use of the
thermodynamic limit. It is further shown that in the case of the 10-states
Potts model as well for the liquid-gas transition in Na, K, and Fe the
microcanonical transition temperature, latent heat and interphase surface
tension are similar to their bulk values for $\sim 200-3000$ particles. For Na
and K the number of surface atoms keeps approximately constant over most of the
transition energies because the evaporation of monomers is compensated by an
increasing number of fragments with $\ge 2$ atoms (multifragmentation).
