The Standard Model of Particle Physics (SMPP) is an enormously successful description of high-energy physics, driving ever more precise measurements to find "physics beyond the standard model", as well as providing motivation for developing more fundamental ideas that might explain the values of its parameters. Simultaneously, a description of the entire three-dimensional structure of the present-day Universe is being built up painstakingly. Most of the structure is stochastic in nature, being merely the result of the particular realization of the "initial conditions" within our observable Universe patch. However, governing this structure is the Standard Model of Cosmology (SMC), which appears to require only about a dozen parameters. Cosmologists are now determining the values of these quantities with increasing precision to search for "physics beyond the standard model", as well as trying to develop an understanding of the more fundamental ideas that might explain the values of its parameters. Although it is natural to see analogies between the two Standard Models, some intrinsic differences also exist, which are discussed here. Nevertheless, a truly fundamental theory will have to explain both the SMPP and SMC, and this must include an appreciation of which elements are deterministic and which are accidental. Considering different levels of stochasticity within cosmology may make it easier to accept that physical parameters in general might have a nondeterministic aspect. PACS Nos.: 98.80.–k, 98.80.Bp, 98.80.Es, 12.60.–i