A purchase money mortgage in Michigan is:

A bank mortgage is an institutional third-party loan where a financial institution lends money to the buyer who then pays the seller in full — this is the opposite of seller financing, and a bank mortgage is never called a 'purchase money mortgage' in the seller-financing sense, even though all mortgages used to purchase property are sometimes loosely called purchase money mortgages.

Government-backed loans (FHA, VA, USDA) involve a third-party institutional lender with a government guarantee or insurance — they have nothing to do with the seller financing the buyer directly, which is the defining characteristic of a purchase money mortgage.

A construction loan is a short-term loan used to finance the building of a structure, typically converted to a permanent mortgage upon completion — it involves a bank or lender, not a seller, and is completely unrelated to the seller-financing concept of a purchase money mortgage.