Budget is a part of profit planning. Sometimes, the budget is a profit plan. There are two approaches, one to estimate sales and deduct all costs and expenses, the result being future profit. The other is to set a profit target and work backward i.e. how much sale level would be required to support so much profit. This is all budget.
But in profit planning we go a step forward and include non-monentrry aspects such as consumer satisfaction, brand loyality, employees' organizational commitment. etc.