A sheriff sale is the end result of a foreclosure action filed by a private entity, usually a mortgage company, after a judgment is obtained against the owner for failure to pay the mortgage.
A tax upset sale vests the buyer with whatever title the former owner had, so if there are mortgage liens, judgments or other incumbrances on the property, the buyer gets the property with all of those things still on there. If property is put up at tax upset sale and not sold, the county can put the property up at judcial tax sale, a more complex process, which results in all liens on the property being eliminated.