Gelman (2005, p. 21) to the rescue.
We prefer to sidestep the overloaded terms “fixed” and “random” with a cleaner distinction […]. We define effects (or coefficients) in a multilevel model as constant if they are identical for all groups in a population and varying if they are allowed to differ from group to group.
Gelman A. (2005). Analysis of variance—why it is more important than ever. Annals of Statistics, 33(1), 1–53