To comprehend the FAA’s definition of Class I or Class II navigation, we must first understand the concept of operational service volume.
Operational service volume is the volume of airspace surrounding an ICAO standard airways navigation facility that is available for operational use. Within that area, a signal of usable strength exists and conforms to flight inspection signal strength and course quality standards, including frequency protection. This describes a three-dimensional volume of airspace. ICAO standard NAVAIDs are VOR, VOR/DME and NDB.
Class I navigation is any en route flight operation that is entirely within operational service volumes of ICAO standard NAVAIDs. Class II navigation is any en route operation not categorized as Class I navigation.
“Class II” Navigation also places a requirement to at least once an hour "Reliably Fix" your position. This will be detailed in your LOA/OpsSpec B034/B050 and B036 authorizations. A more detailed explanation of “Class II” navigation is found in FAA Order 8900, Volume 4, Chapter 1, Section 4.
Inside AC 90-105A (issued back in March 2016) Paragraph 6.5 makes the distinction between Oceanic, Remote Continental, and Offshore operations. It really has nothing to do with a specific number of NM from shore.
Oceanic airspace is defined as international airspace over oceans where separation and procedures are in accordance with ICAO. Controllers provide Air Traffic Services utilizing procedural control and procedural separation.
Remote Continental airspace is defined as airspace above terrain where line-of-sight communications, independent surveillance and reliable ground-based NAVAIDs is not available. Controllers provide ATS utilizing procedural control and procedural separation.
Offshore airspace is defined as international airspace within areas of domestic radio navigational signal or ATC radar coverage, and within which domestic ATC procedures are applied.