The term on the lease for the home I was renting ended on August 31. I gave 15 day notice on the 16th of the month and was out by the 31. I was charged for 15 days rent that went beyond the term of the lease because I did not give 30 days. There was nothing said in the agreement about the lease moving to month to month at the end. Any thoughts would be much appreciated.
Usually leases have language that creates a "holdover" month-to-month tenancy after the lease expires, and that's the law even if it doesn't say so. Your tenancy term is the same term as your payment, and you paid rent every 30 days. Perhaps your lease says something about termination?
As with any contract question, since all contracts are unique and there's no such thing as a "standard" contract, you're best off having someone review your particular contract to see what's been agreed to.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.