An estimate starts with a takeoff of quantities. The estimator then prices labor and material, adds other direct costs and applies overhead and profit.
An estimate is the contractor's own work. A bid or proposal is the price the contractor offers to someone else. The two can differ after management reviews the risk.
Good estimates leave a trail. Record where each quantity came from, by sheet and spec section. Record your assumptions. Another estimator should be able to check your work without calling you.