Here are my thoughts on this subject:
Estimate: 'a judgment of size, number, quantity, value, etc. especially of something that needs calculation or assessment. An estimate can vary, according to context, from a rough guess to close determination'
Budget: 'a written statement of money: where it is drawn from, its amount, how it is to spent (also) to plan expenditure with a given amount of money'
These two words have their context of utilization at different times and from different points of origin. Here is one way to look at these two semi related terms.
First, both terms are guesses. That's right, they both are nothing more than guesses, they both relate to hypothetical numbers (hours or costs).
The term Estimate is 'Doer' oriented. The party (the Doer) that is to do the work makes an 'estimate' of how long they think it will take, how many hours they think it will take, how much material they think it will take, and what they think it will probably cost. Notice these are all 'they think' type of statements; they have not done this actual work yet, so they are guessing. This (Doer) estimating process will use applicable historical data collected over the years. It will also include knowledgeable input from experienced people. It will include prudent contingencies to cover the potential unknowns that occur on every project. In the end, it is still just a guess. It is not the real cost.
The term 'Budget' is 'Payer' oriented. The party (the Payer) who has ordered the work determines how much they are willing to pay for the project. They will do their own estimating to determine what each phase of the project should cost including the engineering phase. They will do some price checking to define what the major equipment and materials may cost. They will also try to determine what the direct and indirect field costs may be. they will have included such things as preliminary amounts for permitting fees, licensor fees, heavy equipment rentals, and third party testing. Being prudent in their thought processes, they will have included factors for what they think they should include for escalation and contingency. They will have determined what they think they should have to pay for the work. This is their 'Budget.' This is also just a guess. It is also not the real final cost.
The real cost of any process plant project is not known until the plant is finished and is successfully running in a full production mode. Billings, charges, and back charges will continue for months after start-up all of which change the final price.
In some cases the Engineering Company will never know the true cost of the project. The Client just does not want that information to be public knowledge. Some project cost information is required for permitting fees and taxation exemptions. For these purposes the client establishes and allows the release of a plant cost that is based on the guesses made early in the project during the estimate and budget process.
Now to your question:"Which tips, procedures, and methods have you found for managing project budgets and making sure that the project comes in as projected."
Start now and collect all the data about every past and present project. Have every discipline reduce their effort down to a single common denominator for their work (Structural = hrs/Tons of steel, Piping= hours/line number (or Iso), etc. there are other factors that effect estimating also. Such as different Clients may "Cost" more than others. Job site location effects cost. Everything effects cost and you should start developing a comprehensive data base for estimating but remember it is still a "Guess".