If ATC is asking for your aircraft type, they would want to know as per the ICAO Aircraft Type Designators (ICAO DOC 8643) so they can input or update your ATC Flight Plan.
If an Apron office is usually the IATA code depending on what systems they are using. This is used for the VGDS (Visual docking guidance system) and stand allocations. Obviously its important to check that the correct aircraft type information is displayed in the VGDS if available before entering the stand as the clearances may be different especially between variants.