Wadiah is safekeeping of a deposit. Such a deposit is hold in trust (Amanah). If the the depositor pays for this favour, the depositary needs to replace it in case of lost. The usage of the deposit is subject to permission of the depositor.
In practical terms the bank client accepts the usage of the deposit by the bank but is not entitled to participate in the profits or losses. The deposit is guaranteed. Some scholars permitted to offer a gift (hibah) for the usage but not as contractual obligation, simply to the sole discretion of the depositary. This account type is quite widespread in Malaysia.