Offshore operations is defined in ICAO Annex 6 (and will be in EASA OPS); there are several linked definitions - they are:
Offshore operations. Operations which routinely have a substantial proportion of the flight conducted over sea areas to or from offshore locations. Such operations include, but are not limited to, support of offshore oil, gas and mineral exploitation and sea-pilot transfer.
Operation. An activity or group of activities which are subject to the same or similar hazards and which require a set of equipment to be specified, or the achievement and maintenance of a set of pilot competencies, to eliminate or mitigate the risk of such hazards.
Note.— Such activities could include, but would not be limited to, offshore operations, heli-hoist operations or emergency medical service.
The term 'offshore operations' is used in Annex 6 (and EASA OPS) as a way of ensuring that appropriate Standards are applied when the majority of flying is over water (in connection with offshore operations).
The text is Annex 6 is sometimes 'open ended' to allow States to extend the definition to include other over-water activities "
which are subject to the same or similar hazards and which require a set of equipment to be specified, or the achievement and maintenance of a set of pilot competencies, to eliminate or mitigate the risk of such hazards" (hence my inclusion of the definition of 'operation').
Under EASA OPS it is likely that 'offshore operations' will require a separate approval (as it does under JAR-OPS); it will set the objective standard (for existing prescriptive rules) and emphasise specific areas of operational procedures and crew training/checking. It is likely that this will be a Subpart under PART SPA and be applicable to all 'offshore operations' - i.e. including also those offshore operations which are not currently conducted/regulated under CAT.
Jim