A 'hardener' usually contains formaldehyde and draws moisture out of the nail ... resulting in harder nails. BUT ... don't over use or the nails become really brittle and often yellow and end up worse than before.
A strengthener is designed to keep the nail tough and flexible and ideally should not contain formaldehyde.
Toughen Up is a strengthener and keeps the nail moist and flexible as well as re-inforcing the cross linking of the keratin layers within the nail plate. Toughen Up contains DMU a patented product which is designed to do this job.