A forecast that always looks a fixed number of months ahead, usually twelve, and is extended by a month each time a month closes.
A rolling forecast keeps a constant horizon instead of stopping at the fiscal year end. Each month the closed month drops off, a new month is added at the far end, and the months in between are updated from the latest actuals. The annual budget stays fixed as the target; the rolling forecast is the current best estimate.
Each cycle: replace the closed month's forecast with its actual, re-forecast the remaining months, and add one month at the end so the horizon stays at twelve. The full-year outlook = actuals to date + forecast for the rest of the year.
After March closes, January to March actual revenue is $2,900,000 and the forecast for April to December is $9,400,000. The full-year outlook is $12,300,000 against a budget of $12,000,000. The rolling forecast also runs to the next March.
Rolling the budget forward unchanged, so it never reflects new information. Updating so often that the team spends the month forecasting. The full guide is budget vs forecast.