ADP is a payroll processor. It is used by some businesses, but not others. Large companies typically handle their own payrolls. Very small companies may have their bookkeeper write checks.
Moreover, many positions, rightly or wrongly, are not W2 positions but 1099 positions.
I'm not sure exactly how ADP comes up with their estimate but I would assume it uses part of its data as a sample and then projects to the entire population. I would assume their statisticians would take care to assure the representativeness of their sample. At a basic level their methodology should be the same that the BLS uses. It is reasonable that their estimates would differ some given they use different samples but over 400% different? Way too much to be statistical noise it seems.