The short answer is yes. You can be on the title or deed of the home as an owner without being on the mortgage. The person who has the mortgage is also an owner of the home. You are co-owners, but not co-borrowers.
There are important implications. The lender who provided the mortgage has a first position lien on the property. If something happens to the borrower, the mortgage company has the right to request payoff of the mortgage. The owner on title may need to sell the house to satisfy the loan payoff, or be able to qualify to get a new loan to cover the value of the remaining loan amount.
This kind of problem occurs in a variety of situations. For instance, if parents put their adult children on the deed to a home as a method of handling inheritance, but the kids are not able to satisfy the loan requirements if the parents pass away or become incapacitated. Let me know if you have other questions or need help moving. Valerie, (718) 399-3320