No “owning” a house that is 80% owned by a bank?

That's not how mortgages work. Your name is on the title/deed? You own it, for realsies.

If you have not paid in cash, the property may also be used as collateral for the loan acquired to purchase it. When this is the case, the title/deed has a lien placed on it, so that when the property is sold, the lienholder is repaid first from the proceeds of the sale - again, because the property is being used as collateral.

If you fail to meet the terms of the loan, the mortgage holder (probably not a proper bank) can take possession of the property, for the purposes of selling it to recover the unpaid portion of the loan. If the sale of the property recovers more money than the outstanding balance of the loan, the original owner gets the difference. This is foreclosure, and mortgage holders do not want to do this, for a number of reasons.

• When the mortgage holder forecloses, they now bear the expense of selling the property. This means making it ready for sale, paying a realtor fee, being responsible for property taxes, HOA dues, lawn maintenance, any necessary repairs. (If they don't pay for these things outright, there will be concessions given to the buyer to cover them.)
• Foreclosed properties often sit empty for a good period of time. Maybe the original owner moved out before the foreclosure was completed, and the property will often sit before going to market, then after as well. Until the property is sold, it is a pile of potential money, which nobody is repaying a loan for.
• In order to reduce the amount of time this asset is on the books, the mortgage company is likely to sell the property for less than it would get if it was being sold by a homeowner.
• Foreclosure is far more likely to happen when a mortgagee (homeowner) has bought the property when the market is high, and is unable to repay the loan at a time when the market is low. If things were the other way around, they would simply sell the property, pay the balance of the loan, and take the difference in cash. A mortgage holder does not want to take possession of a home that is worth less than what is owed on it (also taking into account all of the foreclosure costs above); they would much prefer to continue to receive mortgage payments.