NP-completeness is a property of problems, while BQP is a complexity class (set of problems). If any NP-complete problem is in BQP, then NP is a subset of BQP.

NP-completeness is a property of problems, while BQP is a complexity class (set of problems). If any NP-complete problem is in BQP, then NP is a subset of BQP. But it's not even known whether BQP > P, so we could have P = BQP < NP.