(Financial) The budget is a financial statement that estimates and details the planned income and expenses for a particular period of time. In some contexts the budget is just the expense line items without any associated income – for example the “marketing budget for this year.”
In many organizations budgets are developed annually and represent hard and fast spending limits – “we have exhausted our recruiting budget with still two months and ten hires to go.”
(Grants) A grant budget is the financial plan for a project or program from beginning to end. In grants the details of what the grant money is spent on versus what other sources of project or program funding are spent on can become quite extensive.