A mortgage note is the written instrument in which a borrower promises to repay money borrowed to buy or refinance real property, on terms the note itself sets out. It is usually titled just "Note", and it is one half of a pair: a mortgage takes both a note and a security instrument, and the security instrument, called a mortgage in some states and a deed of trust in others, is what pledges the house. The note says what is owed and how it is to be paid. The security instrument says what the lender may do to the property if the note is not paid.
California's Commercial Code puts the definition in a single clause. Under section 3104(e), an instrument "is a 'note' if it is a promise". The word "instrument" is doing work there: subdivisions (a) and (b) of the same section define it as a negotiable instrument, meaning "an unconditional promise or order to pay a fixed amount of money" that meets the section's other conditions. The same section, at subdivision (a)(3)(i), allows that promise to carry "an undertaking or power to give, maintain, or protect collateral to secure payment" without ceasing to qualify. That is the statutory reason a mortgage note can point at a house and still be a note rather than a hybrid: the collateral is referred to, not incorporated.