Budgets are set before a financial year begins and are not adjusted after they are approved.
Forecasts track what you know as the financial year unfolds.
Budgets allow management to control costs from the bottom up. It is critical for a business to maintain control of the budget to enable management to form a view on which costs are truly fixed versus those that are variable. For example a person on a fixed salary versus a casual employee who can be scaled as income scales.