"Convective" heat transfer includes heat transfer by both advection (the bulk fluid movement) and conduction. You might think convection is just advection, and I will admit the terminology is used inconsistently.

Thanks for the correction, I was also watching PBS Space Time on Red Dwarfs, and how small stars cool the core by convection. Larger stars use radiation in the core and so lose access to a majority of the mass of the star which could have been used for fuel.