Yes, there is a difference between business risk and project risk, and as the project manager, you should care about the differences.
Business Risk
Business risk involves creating the right project output to address a specific business need. Business risk is not typically the responsibility of the project manager.
Business risk is generally managed by the project owner, project sponsor, or stakeholders.
Project Risk
Project risk relates to ensuring the project produces the promised results on time and within budget.
Project risk is definitely the project manager’s responsibility.