Questions about spin glasses often involve an optimization problem in a discrete space, but many of these problems become more tractable when we consider a continuous analog. Discrete and continuous spin glass models share many properties, but there are also striking differences. This talk will focus on a specific example: Free energy fluctuations in the Sherrington-Kirkpatrick (SK) model and its continuous analog, the spherical SK model. I will provide an overview of some known results in this area, highlighting similarities between the two models at high temperature as well as differences that emerge at low temperature. In that context, I will discuss my work on free energy fluctuations in the bipartite spherical SK model at critical temperature (joint with Han Le).