What is the difference between a budget and an estimate?

The Budget is the final step (aggregation) of cost estimates.

Budget : is a quantitative expression of a plan for a defined period of time.Estimation : is the process of finding an estimate, or approximation, which is a value that is usable for some purpose even if input data may be incomplete."Look Source"

Budget is a summary of probable income and expenses for a certain period of time whie estimate is a valuation based on opinion or roughly from imperfect data or incomplete data.

Budget is an estimate of costs, revenues, and resources over a specified period, reflecting a reading of future financial conditions and goals. Otherwards it is the financial plan for a fixed period of time.

One of the most important administrative tools, a budget serves also as a (1) plan of action for achieving quantified objectives, (2) standard for measuring performance, and (3) device for coping with foreseeable adverse situations.

 Estimate is Approximation, prediction, or projection of a quantity based on experience and/or information available at the time, with the recognition that other pertinent facts are unclear or unknown. An estimate is almost the same as an educated guess, and the cheapest (and least accurate) type of modelling.

Budget is an estimation of the revenue and expenses over a specified future period of time, can be made for a person, family business, government, country.  while Estimate is an approximation of the probable cost of a product, programe, or project , computed on the basis of available information

An estimate is a "ball park" calculation to determine how much something will cost. A budget is the amount of money that you put aside to cover that cost.

Estimate is the rough sketch of expenses , It is not  as accurate  to form a basis for a firm commitment. First step for budget preperation. A cost estimate is used to evaluate the required funding and to compare with bids or tenders. A cost estimate is often used to establish a budget as the cost constraint for a project or operation.

Budgets are approved expenses allocated for certain work/activity/purpose with guideline, how it can be used and who is allowed to approve for actual expenses. A budget is a quantitative expression of a plan for a defined period of time. It may include followings :

a) Planned sales volumes and revenues,

b) Resource quantities,

c) Costs and expenses, assets, liabilities and cash flows.

It expresses strategic plans of business units, organizations, activities or events in measurable terms.

Budget is fixing an amount for future expenditure..whereas estimate is calculated for a price of an article or goods to be supplied.

For a new construction project, a budget is a financial plan comprising allocated funds intended for that particular project, calculation of which is based on the cost data obtained from previous projects with similar type of structure and requirements. However, adjustment of previous cost data has to be made to reflect the current conditions relative to prices. Once the budget is established, a system has to be implemented to contol expenditures to avoid exceeding the budget as much as possible. 

When a bidding is to be conducted, both sides, i.e. Project Owner and Bidders/Contractors have to prepare detailed estimates. Bidders will submit bids containing said detailed cost estimates which will be the primary basis of bid evaluation and comparison. The Project Owner will then examine the comparison between his cost estimates and the cost estimates from bidders, and relate it to the established budget.

Budget is a formal and approve document & Estimate is Approximately opinion

BUDGET IS AN ALLOCATION OF RESOURCES FOR A SPECIFIED TIME(ACCOUNTING PERIOD)  UPTO A  SPECFIC LIMIT WHETHER A ESTIMATION IS A TECHNIOQUE WHICH ESTIMATE THE COST OF A PROJECT WHICH IS COMPLETED WITH IN A TIME LIKE2,3,4 MONTHS.