This is not true, with leasing you don't own the product or property at all. Leasing is basically long-time rent. For example, when you lease a car, you don't own it - the leasing company does. In some cases, you can buy out the object at the end of the lease (like cars), in some cases you can't (like apartments).

> a financial construction where you actually own the product / property, with the bank having the option to claim it if you fail to pay.

This is called financing - basically, buying a thing with bank's money which they give you as a loan. For high-value purchases, there are often limitations on what you can do with the object, or requirements (like a requirement to have homeowner insurance for mortgages), but there are usually less restrictions compared to lease since you are the owner.