Do people talk about "inductive definitions"? I mostly only hear about induction in the context of proofs, in which case I'd say that an inductive proof/argument is one that uses the recursive structure of whatever it's about.
A recursive definition is: "natural numbers are 0 or a natural number + 1". An (abridged) inductive proof that uses the recursive nature of natural numbers: "the sum of all naturals up to n is n(n+1)/2: 0*(0+1)/2 = 0, and (n+1) + n(n+1)/2 = (2(n+1) + n(n+1))/2 = (2n + 2 + n^2 + n)/2 = (n^2 + 3n + 2)/2 = (n+1)(n+2)/2 = (n+1)((n+1)+1)/2"
A recursive definition is: "natural numbers are 0 or a natural number + 1". An (abridged) inductive proof that uses the recursive nature of natural numbers: "the sum of all naturals up to n is n(n+1)/2: 0*(0+1)/2 = 0, and (n+1) + n(n+1)/2 = (2(n+1) + n(n+1))/2 = (2n + 2 + n^2 + n)/2 = (n^2 + 3n + 2)/2 = (n+1)(n+2)/2 = (n+1)((n+1)+1)/2"