Each answers a different commercial question. Blending them together is one of the fastest ways to make a construction forecast look better than the project actually is.
The budget is the approved cost plan. It creates the baseline against which procurement and forecast movements are measured. A budget is not proof that the work can still be bought for that amount.
Committed cost captures awarded subcontract packages, purchase commitments and other obligations before every dollar is invoiced or paid. This matters because an accounting ledger can still look clean while the commercial obligation already exists.
Actual cost is historical. It is essential for reconciliation, but by itself it cannot tell you the final outcome of an incomplete project.
Suppose a trade budget is $100,000. Only $20,000 has been invoiced, but a subcontract has already been awarded at $115,000. Looking only at actual cost says the trade is 20% spent. Looking at the commitment says the project has already locked in a $15,000 budget overrun before the remaining claims arrive.
Some work will remain outside current commitments. That scope still needs a realistic cost-to-complete allowance. Otherwise the project forecast quietly assumes unprocured work will cost nothing, which is ambitious even by construction standards.