This ignores the history and historical purpose of the Marines and actually isn’t correct for members of the Imperial Japanese Military in WWII, either. The Imperial Japanese Navy had infantrymen who were not called soldiers.
I believe that the Royal Marines are not called “soldiers”, either but are called “Marines.”
The purpose of the US Marines was (from Wiki)
They are not simply an army with another name.
They have a distinct purpose and command, falling under the Navy rather than the Army.
They are used in an expeditionary role. While that role have been fallen to particular army units in other countries, in the US military, it was given to the Marines.
Hence, the Marines were sent to fight against the Barbary Pirates in the early 1800.
In the US Civil War, they weren’t given much of a role but later were used in the banana wars the US had in Central America.
After WWI and before WWII, the Marines were looking for more of a purpose and started to develop doctrine and training for amphibious warfare.
In the Pacific War, the Marines started the counter offensive with the invasion of Guadalcanal, and from there they conducted the famous island hopping campaign through to Iwo Jima and Okinawa.
There is a lot of mythology that developed around the Marines during the war, and most people don’t know that more Army personnel served, fought and died in the Pacific War than Marines.
The popular narrative is that the Pacific War was fought at Sea by the Navy and on land by the Marines, and the Army’s role gets shortchanged.
The Marines were not just another army. They lacked the self sufficiency in logistics, for example, and were dependent on the Army and Navy for these things.
The interplay and rivalry between the various service branches is fascinating (for people who are interested in such things).