Legal Question in Landlord & Tenant Law in California

It is considered "month-to-month" because it is paid monthly and has no expiration. "Month-to-month" really is not a legal term. It is not a 60-day lease either, because it does not expire at the end of 60 days. The technical legal term is a "tenancy at will." In any case, however, the exact label is irrelevant. What counts is the agreement and any law that supersedes any term of the agreement. In your case you have each agreed to give 60-days notice of a termination of the tenancy. That is perfectly legal and binding. As for how much notice the landlord must give, in the absence of any terms in the agreement, the landlord must give 30-days notice of any change in the terms or conditions of the tenancy if you have lived there less than a year, and 60-days if you have been there more than a year.