If aren't they synonymous, what distinguishes the one from the other? Is probability density estimation a certain kind of generative model? Can any generative model be regarded as density estimation?
Density estimation is generally seen as a nonparametric goal: rather than using specific families such as the Gamma family or the Normal family, density estimation procedures can arrive at any shape. I haven't seen anyone use the name "density estimation" for a parametric procedure, presumably because then it's just parameter estimation.
By contrast, generative models often have parametric components; for example, the Latent Dirichlet Allocation model uses the Dirichlet distribution.