Initially there was little difference between soldiers and sailors when it came to naval combat. Being relatively poor sailors when compared to Carthage, the Romans invented the Corvus. The Corvus (meaning "crow" or "raven" in Latin) was a Roman naval boarding device used in sea battles against Carthage during the First Punic War. 
This allowed the Romans to treat sea warfare like land warfare which they excelled at.
The first organized marine corps was created in Venice by the Doge Enrico Dandolo when he created the first regiment of ten companies spread on several ships. That corps participated in the conquest of Byzantium (1203-1204), later officially called "Fanti da Mar" (sea infantry) in 1550.
The word marine was originally used for the marine-type forces of England; however, the word marine or marina means "navy" in many European languages, including Dutch, French, Italian, German, Spanish, Danish, and Norwegian. The term for what we think of as a marine translates into English as naval infantry or coastal infantry. Marines, or naval infantry, are typically a military force trained to operate in littoral zones in support of naval operations. Historically, tasks undertaken by marines have included helping maintain discipline and order aboard the ship (reflecting the pressed nature of the ship's company and the risk of mutiny), the boarding of vessels during combat or capture of prize ships, and providing manpower for raiding ashore in support of the naval objectives. In most countries, the marines are an integral part of that state's navy.
This makes sense as their mission requires skill sets not found in the Army. Marines operate in and about the coastal regions of the world. The United States Marine Corps (USMC) is currently the only marine combined-arms force in the world. Created in 1775, it was originally intended only to guard naval vessels during the American Revolutionary War. I personally think they need a bumper sticker that says "The USMC Going Coastal since 1775."
As for who selected the name, I'm not sure. We inherited it, along with almost every other standing tradition, from the Royal Navy when we gained our independence. Given the time period, the RN was a good place to look for inspiration.
WWG1WGA
Garde la Foi, mes amis! Nous nous sommes les sauveurs de la République! Maintenant et Toujours!
(Keep the Faith, my friends! We are the saviors of the Republic! Now and Forever!)
LonePalm, le Républicain du verre cassé (The Broken Glass Republican)