If you fail to satisfy your mortgage agreement with the bank, then yes, they can take the house from you in a foreclosure. But until then, it's yours, not theirs.
A lienholder is a lender that legally owns your property (a car, for example)
until you pay it off in full. The lender — which can be a bank, financial
institution or private party — holds a lien, or legal claim, on the property
because they lent you the money to purchase it.
https://www.allstate.com/tr/car-insurance/learning-about-lie...Edit: legally they DO differ, but they're the same in that they allow the lender to take back the property in the event of non-payment. Therefore, even though you might legally technically own a property with a mortgage, the bank still has the ability to take it away from you, so do you REALLY control it? https://www.quora.com/How-do-a-lien-and-a-mortgage-differ
I understand the point being made. It's a commonly held opinion, and it's fine for inspiring people to get out of debt, but legally it's not correct. Your home is your property, even with a mortgage.
Also, a foreclosure is not the only way to lose your property. Stop paying your taxes and see what happens. Even unpaid unsecured debt (like credit cards) can lead to your home being taken in some situations. Or the government can take your property via eminent domain.
So there is no such thing as REALLY controlling property, in terms of excluding any way it can be taken from you. But you do have specific legal rights to your property, and those apply to mortgages too.