You asked, "Am I correct in thinking that a 'Sea going Marine' wore a different colour uniform to an 'Army Marine".
Simple answer No.
Firstly although in the days before the initial 50 companies of HM Marine Forces were formed in 1755, detachments of army regiments served aboard ships as "marines" the army soldiers and Royal Navy's marines are different branches of the armed services.
In 1855 the Corps of Royal Marines was designated a 'Light Corps' with the title Corps of Royal Marines' Light Infantry (RMLI) and continued to wear the distinctive Red tunic of British Infantry regiments, that had led to the Royal Navy's "blue jackets" (seamen) referring to them as Lobsters. The RMLI was still organised in the RM's original Grand Divisions of Chatham, Plymouth & Portsmouth.
In 1859 a new division was formed at Woolwich, the Royal Marine Artillery. Like the army's Royal Artillery they wore Blue tunics. Not to be confused with the RN's seamen, the RMA became known as the Blue Marines and the RMLI the Red Marines; detachments of both the RMLI & RMA served at sea and on land, hence their motto Per Mare Per Terram (By Sea By Land).
in 1923 the two branches of the RMLI & RMA were merged to become the Corps of Royal Marines.