Answer
Attribute sampling tests the rate of occurrence of a characteristic—used in tests of controls to estimate the deviation rate (a yes/no attribute like 'was it approved?'). Variables sampling estimates a numerical amount—used in substantive testing to estimate monetary misstatement. Attribute answers 'how often?'; variables answers 'how much?'.
Real-world example Attribute sampling measures how often approvals were missing; variables sampling estimates the dollar misstatement in balances.