Budget means both expenses and revenue. In quite a few cases, say personal finance, typically one refers to budget more from expenses point of view as the revenue is typically fixed/known [mostly salary].
The Operating budget and capital budget are laid out separately as Operating budget gives out day to day expenses that are typically essential, employee salaries, routine maintenance of infrastructure etc. The revenue is also tied in to match this. These are done within the same year.
Where as capital budget is to build new infrastructure say a new bridge or other major expense that are done over period of years. The revenues to this are typically tied up differently and can even be linked to getting more funding from other agencies or loans.