What is the difference between an Ijara (lease) contract that ends in ownership and a diminishing Musharaka (partnership) that ends in ownership, and what are their legitimate Shariah controls?

The difference between an Ijarah Muntahia Bittamleek (Lease Ending in Ownership) contract and a Diminishing Musharakah (Diminishing Partnership) is that the former's subject is a leased asset that typically transfers to the lessee at the end of the contract for a price or as a gift, whereas the latter's subject is a jointly owned asset where one partner's share gradually transfers to the other. In a Diminishing Musharakah contract, the partner may lease the other partner's share before acquiring full ownership, thus becoming an Ijarah Muntahia Bittamleek.