Means-tested social benefits refer to benefits where entitlement is explicitly or implicitly conditional on the beneficiary's income/wealth.
This covers cases where income/wealth is used to determine (1) only entitlement or (2) both entitlement and amount. The latter case refers to a benefit that is degressively linked to income/wealth and reduced to zero as income rises, the point at which the amount tapers to zero being the level of income/wealth at which there is no entitlement.
Benefits where income/wealth is used to determine only the amount of benefit received (i.e. degressively linked to income/wealth but only to a certain minimum level so that there is always some entitlement) are not considered to be means-tested.