Is it common to refrigerate after 2F with ginger beer?

I've been having luck brewing kombucha this past year and am interested in trying out ginger beer since I have been lead to believe the processes are quite similar (besides the 1 way valve for 1F). Whenever I've brewed kombucha I've stopped 2F after 3-5 days simply by putting the bottles in the fridge. However, I've read a few instructionals on ginger beer that recommend pasteurizing. Is there a difference with a ginger beer bacterial culture (vs a SCOBY for reference) that would cause it to continue fermenting substantially at fridge temperatures?