I have a specification that references ICC 500 and FEMA 361. Are these the same?

No, they are not the same, but they are both related to the construction of tornado shelters. FEMA 361“Design and Construction Guidance for Community Safe Rooms” is a guidance document, but FEMA does not regulate building construction. ICC 500 “Standard for the Design and Construction of Storm Shelters” is written by the International Code Council® and is referenced in the International Building Code in all Editions since 2009.