Both are relating to the estimation of future but , if we deeply study the both concept we can get following differences between them. :-
Related : Govt. Budget
1st Difference
Budget is based on planned events . We actually makes stand in advance and then control our position
forecasting is just estimation of uncertain future for making planning .
2nd Difference
Budget is made for one financial period
Forecasting is for long time.
3rd Difference
It is necessary for budget or corporate to make budget
forecasting is suitable in that field where we do not make budget.
Related : Govt. Budget