These terms sound similar but can mean very different things.
Lead-based paint has a specific regulatory definition. In California, it generally means paint containing at least 0.5% lead by weight or 1.0 mg/cm².
Lead-containing paint is a broader descriptive term that may be used when laboratory analysis detects lead at some concentration, even when the concentration is below the regulatory lead-based-paint threshold.
Therefore, a paint sample can contain measurable lead without meeting the definition of lead-based paint.
Understanding the actual laboratory concentration is more useful than simply asking whether lead was "detected."