The Budget is the main body of information for reporting the anticipated performance of your organisation, against what actually happens over a period of time.
A Scenario (you can have as many as you like) is an additional layer of activity you can add to the underlying budget. Each scenario represents a small change, like:
Adjusting costs for a new project
Increasing revenue for a potential contract
Taking on additional Staff, accounting for Wages / Superannuation / Workcover / Operational costs etc.
You can create multiple scenarios and apply them individually or in combination to see their impact on your overall budget. Thery can be Previewed in the Budget screen or included in any of the Dashboards and Reports. See the Scenarios: Overview help article for more details.