As adjectives the difference between grounded and stable
is that
grounded is (aviation|of an airman) not allowed to fly while
stable is relatively unchanging, permanent; firmly fixed or established; consistent; not easily moved, altered, or destroyed.
As verbs the difference between grounded and stable
is that
grounded is (
ground) while
stable is to put or keep (horse) in a stable.
As a noun stable is
a building, wing or dependency set apart and adapted for lodging and feeding (and training) animals with hoofs, especially horses.