Project manager

Sir bpp gives the following definitions of projext manager and board
The project manager takes responsibility for ensuring the desired result is achieved on time and within budget.
The Project Board (PMBOK: project steering committee) is the body to which the project manager is accountable for achieving the project objectives. It represents the interests of the project sponsor.

One is saying manager is responsible for meeting time and budget constraint and other is saying objectives achievment. So what really is the clear definition?