Business and government budgeting are more different than alike. Government budgeting is preoccupied with allocating scarce resources among many competing demands. Unlike the government, the revenue of a business is not constrained; a business can do many things to increase sales revenue.
From federal agencies down to local school districts, government entities have only so much revenue available. They have to make difficult choices regarding how to spend their limited tax revenue.
Formal budgeting is legally required for almost all government entities. First, a budget request is submitted. After money is appropriated, the budget document becomes legally binding on the government agency. Government budgets are legal strait jackets; the government entity has to stay within the amounts appropriated for each expenditure category. Any changes from the established budgets need formal approval and are difficult to get through the system.
A business is not legally required to use budgeting. A business can implement and use its budget as it pleases, and it can even abandon its budget in midstream. A business can pass its costs to its customers in the sales prices it charges. In contrast, government has to raise taxes to spend more (except for federal deficit spending, of course).