There are three mechanisms by which energy transport occurs inside of a star: convection, radiation transport, and conduction. For Main Sequence stars, conduction is not important. Conduction is important in stars like white dwarfs.
Whether, convection (circulations) or photons (radiation transport) carries the energy is determined by which process is more efficient (hmmm, this is a pretty obvious statement, isn't it?). Effectively how this works out is if the star needs to transport a lot of energy quickly and the opacity (the probability of absorption or scattering) is high, then the energy is carried by convection. If the opacity is low, then it is more likely for the energy to be carried by photons.
For stars, this leads to different structures for Main Sequence stars depending upon their masses. Recent Hubble Space Telescope press release on the structure of low mass stars and some things learned using the Hubble Space Telescope.
