This post applies only to those of us who rely mainly on Ancestry.com for census records. There, the 1820 Highland County census was merged with the Fayette County census. Such townships as Brush Creek, Jackson, Liberty, the Town of Hillsboro, etc, are Highland. There are four township names which both counties use: Concord, Madison, Paint, and Union. All four are listed as Fayette but if you look at the frames, you can see that Fayette County's township is first and then Highland's.
For example, if you look up someone and are taken to Paint Township, Fayette County, there are 6 frames for Paint of Fayette followed by 7 frames of Highland County's Paint. The relevant frames would be 7-13 the last of which concludes Paint and begins Liberty.
The Fayette lists and Highland lists are in distinctly different handwritings. Fayette lists will be marked with a numeral and a letter such as 6A as the first page of Paint. The Highland entries will be marked with a numeral such as 17-23 for Paint.