Intuitively induction is for reasoning about all possible values of an inductive type. Inversion is reasoning about a particular « shape » of a term of an inductive type.
For instance if you have a hypothesis of type:
H: S n <= m
And you want to deduce that « m has necessarily shape S m’ for some m’» then inversion (on H itself) is enough. Because just matching the possible constructors for H gives that immediately.
On the other hand if you want to deduce from the same fact that n <= m then you need induction (on H itself) because it does not only follow from the shape of constructors but from the fact that unfolding constructors will eventually end up with a base case (which is the raison d’être of induction/recursion)
Hope I gave the intuition but anyways it is not always clear that a property is of one kind or another. And anyways sometimes using an already established lemma avoids induction or inversion completely.
EDIT: note that if you want to prove the inductive property above you may have to first manipulate H to be of the form n’ <= m.