We investigate the potential of a future supernova data set, as might be obtained by the proposed SNAP satellite, to discriminate among different "dark energy" theories that describe an accelerating Universe. We find that many such models can be distinguished with a fit to the effective pressure-to-density ratio w of this energy. More models can be distinguished when the effective slope dw/dz of a changing w is also fit, but only if our knowledge of the current mass density Omega(m) is improved. We investigate the use of "fitting functions" to interpret luminosity distance data from supernova searches.