They are supposed to be Navy (their uniforms claim Navy) but they keep interchanging terms and slogans for the Marines such as "Semper Fi".
The United States Marine Corps can be seen aboard two types of large vessels: Amphibious Command Ships and Amphibious Assault Ships. The Blue Ridge-class Amphibious Command ship gives Navy and USMC leaders an amphibious command base where they can coordinate with fleet commanders during operations. There are only two of these, the USS Blue Ridge and USS Mount Whitney. The amphibious assault ships, whether Tarawa, Wasp, or America-class, look like smaller aircraft carriers with flight decks where Vertical Take-Off and Landing aircraft can land and depart from but they're more favorable than full-sized carriers as they provide a means to get troops and vehicles from the sea to the shore.
At no time in the history of the United States of America have the US Marines had any of their own ships. The US Navy is the Uber for the US Marines.