Delhi Township, like all townships in Ohio, operates/spends from the appropriations the Trustees approve each year. Appropriations are what money is appropriated(allocated) from each fund and specifically each line item to pay for expenses and obligations. The Township Administrator is responsible for presenting the overall appropriations to the Trustees for their consideration and approval and the Township Administrator is also responsible for initially approving spending requests from each department. The Fiscal Officer is responsible for managing the accounting of funds, spending requests meeting the state auditor's guidelines, and balancing the bank statement.
The above, briefly outlined description, is what some would simply refer to as budgeting or the budget. Therefore, you may see the word budget or appropriation used in similar context and they mostly mean the same thing. Also, the explanation above highlights the function of the separately elected Fiscal Officer. The Trustees appropriate and approve 'spending' the township funds while the separately elected Fiscal Officer accounts for the funds and their use from an accounting standpoint.