IRS is Class. Owners are free to choose any Classification Society on the list of Class approved by Administration. Usually good operators choose a IACS member. IRS is RO if IRS is empanelled by Administration of the Vessel. Role of RO is to issue statutory certificates on behalf of Administration. Such certificates issued by RO contain a line on header on page one “Issued under the Authority of xxx” See sample cetitiicates in SOLAS / MARPOL IRS is on RO list by India, even EU countries. It is possible to engage separate Class and RO but for convenience it makes better sense to have same org as both. Same attending surveyor can handle both Class and RO issues. DGS/ MMD is the Administration. If cert is issued by MMD, it itself is Administration. It is not RO.