Diminishing Musharakah is where the Bank and you become joint owners of an asset, and the Bank’s share is further divided into a number of units. The contract lets you buy the Bank’s share at a pre-agreed price, or at market price, or at a price agreed upon at the time of sale. The Bank earns a profit from renting you its share until the title of the asset is completely transferred to you.
Ijarah is a leasing contract. The Bank buys the asset and leases it to you with the promise to transfer ownership to you at the end of the Ijarah contract term through an independent sale transaction.