On the 1860 Lawson was only 8, so I wasn't expecting him to be on the 1850 census, but Lawson age on later censuses would indicate he probably was born prior to the 1850 census.Yes, I've often found people using first name on one census, middle name on the next and sometimes back and forth.
My husband has ancestors counted in different counties on the 1870 census, and youngest child is not on one of them.The 1850 census was supposed to be as of the first of June, so Lawson may have been born after the first of June, and wasn't counted on one census, but enmurator counted him on the second one, as he might not have gotten around to the household until later in the year.Who knows.On the other hand, there could be two Andersons, maybe cousins, who had been named after their common grandfather???
I would check out records in that county in GA where you found one of the Andersons on the 1850 census.Post queries for that county, see if anyone else is working on the Sneeds in that area.
Did you check land and probate records for Anderson in FL?His heirs should show up, as they would have to sign off on the final sale of that land to give clear title to the buyer.