False.
This is a periodic tenancy because Tom, as the tenant, may rent the apartment for successive periods under his lease, despite being "month-to-month." A tenancy at will, however, allows either the landlord or the tenant to terminate the arrangement at any time because there is more flexibility in the arrangement.
One key difference is the issue of the tenant's notice to vacate the apartment. Under periodic tenancy, the law typically requires the tenant to give at least one period (here, one month) notice to the landlord of the tenant's wish to leave the property. No such notice requirement is typically found within a tenancy at will.