I found the following from an article on-line at http://www.usgwcensus.org/help/1.htm that I think will help explain the census use of beats, districts, etc.:
From The SOURCE A Guidebook of American Genealogy (Revised Edition: Edited by Loretto Dennis Szucs and Sandra Hargreaves Luebking, Ancestry, Published 1997) page 104:
"In the days before regular mail service, government representatives conducted door-to-door canvasses of their appointed districts. Supervisors subdivided districts using existing local boundaries. The town, township, military district, ward, and precinct most often constituted one or more enumeration districts.
Boundaries of towns and other minor civil divisions, and in some cases of counties were ill defined, so enumerators were frequently uncertain whether a family resided in their own or an adjoining district. For this reason, it is not unusual to find individuals and families listed twice in the census and others missed entirely."
In most years and in most places, the census was taken on a county by county basis. In a few states and territories, such as Arizona, Louisiana, Orleans, South Carolina, and others, the county divisions have been known by other names. In other places in some years, counties have not existed or have not been used, so other means of dividing up the state or territory have been used. Common examples of these names are Beat, Division, Judicial District, District, etc.
Within the county or other major civil division many subdivisions have been used. These incluse Township, Precinct, City, Town, Village, District, Division, and Ward. From 1880 on, enumeration has been done by ED, or enumeration district.
EDs, strictly defined, were not used until the 1880 census. The early censuses used the term subdivision to refer to part of a supervisor's or marshal's division or district. Subdivisions in the early censuses comprised towns, townships, or other units comparable to MCDs (Marshall's Census Divisions or Districts).
Most early ED descriptions are general and largely served as documentation of the names of enumerators and rates of pay. They may simply state that a census taker had to enumerate an entire county or an unspecified part of a subdivision. Beginning with 1850, the ED descriptions became increasingly detailed.
A supervisor's district is a large geographic area that usually covers several counties.
Each state was divided into one or more large districts (SD's), then each of those into hundreds of individual districts (ED's), one per enumerator usually. So in a large state there will be several ED's, 47 for instance, in each SD. We are going to divide states into multiple pages (In our Table of Contents), and the SD is how we should do it, therefore we need to know which counties are in which SD.
An Enumeration District (ED) refers to the area assigned to a single census-taker to count persons and prepare schedules within one census period. It is very important to become familiar with the ED's used in the state and census year that you are transcribing (they usually differ from year to year).