The comments about 1820 through 1840 only listing heads of household, 1850 through 1870 listing everyone in the household but without family relationships, and 1880 including family relationships is true for all states, not just Tennessee. The comments about missing counties and missing censuses are fairly specific to Tennessee. But many other states and counties have missing data from the early censuses as well. For example, some of the early census data was burned by the British when they sacked Washington, D.C. during the War of 1812. They burned the census data at about the same time they were burning the White House.1790, 1800 and 1810: Tennessee became a state in 1796. The territorial census schedules and the 1800 census were lost or destroyed. The 1810 census of Tennessee was also lost, except for Grainger and Rutherford counties, which have been indexed.
1820: This census is incomplete and most East Tennessee counties are missing.
The censuses for the year 1820 through 1840 only list the name of the head of household. Others in the household are only counted by age category, male and female. There are no family relationships in these records and no names other than the head of household.
It wasn't until the 1850 census that the names of everyone in the household were listed with their age and state of birth. No family relationships in this one either. It remained the same for the 1860 and 1870 census. In 1880 the state of birth of parents was added along with the relationships of those in the household.