Hoosier, when you use the word “note” in that context, you are speaking about a promissory note. That would be a contract that outlines money owed, how much, the interest rate, due date, etc.
Beyond that, I am not quite sure what sort of situation you are trying to get information about.
I think the idea behind “carrying the note” is holding the loan on the property. For example, if you own a property and have no loan on it, you could sell with your financing and “carry the note.”
The situation you describe is putting the house in service as a rental, then later selling the house to your tenant with seller financing some portion of the sale.
The lease arrangement could be either a straight lease or a lease with option to purchase. The sale to your tenant could be financed by (1) buyer’s new mortgage loan for a portion of the purchase price and you hold a second mortgage for the balance of the purchase price, or, (2) a wrap-around mortgage for the full purchase price, or, (3) a contract for deed for the full purchase price.