Both time schedules depend on different elements. This would be why the time estimates needed for both would be fundamentally different. Time estimates for scheduling are contingent on manpower, human resources, sometimes even external conditions, as well as elements that can be negotiated to a certain extent because they are contingent on people and individuals. The time estimates for budgeting are a bit different. Here, money and sources of funding or revenue streams are the fundamental concerns. These can take on a different life because they are not only contingent on individuals, but also on other elements such payment delivery and ensuring that transfer of money from one perspective to another is complete. I would think that budgeting time estimates have to remain separate from scheduling estimates. They do not have to be in opposition to one another, but they are dependent on different factors.
The nature of any estimates including those for budgeting and scheduling depend on the purpose for which the estimates are used. The nature of estimates may be determined in terms of variables like:
Quantities estimated: This can be money, time, material, manpower, sales or any other input resource, or output generated.
Extent of Detail: For example the production output may be estimated for each component to be manufactured or in terms of total value of products to be manufactured.
Degree of accuracy: An estimate of material required used for a preliminary feasibility report is not required to be very accurate, as compared o the estimate used for actually placing purchase order for procurement of some material.
It is not possible to distinguish an estimate prepared for scheduling from that for budgeting by just looking at the nature of the characteristics of the budget. An estimate with comparable characteristics may be used for scheduling, budgeting, or any other purpose. However assuming that scheduling is a shorter term and more detailed exercise as compared to budgeting, the estimate for scheduling are likely to be more detailed and accurate.