"2d Marines" indicates 2d Marine Regiment. "6thHQ(?) 2d Marine" may represent "Headquarters Company, 6th Marine Regiment, 2d Marine Division". No way to tell from the info you've provided. The 2d and 6th Marines were (and are) two of the division's three regiments of infantry (the 8th Marines was - and is - the other). The 4th Marine Division (23d, 24th & 25th Marines and supporting elements) and the Army's 27th Infantry Division (105th, 106th & 165th Infantry and support) also participated in operations at Saipan.
Marine regiments are designated "Marines" in the same manner army regiments are referred to by arm of service (1st Artillery, 1st Infantry, etc.). Marine Divisions and Marine Brigades are always referred to as such - never as "Marines". This eliminates any doubt or confusion as to the type of unit you're referring to.