Yes, that's correct.
While it does seem a bit complicated in the beginning, think of it this way.
A marine license allows you to transmit on the marine bands only.
A ham license allows you to transmit on the ham bands only.
You can listen anywhere.
You can use any radio on the ham bands.
On the marine bands, you can only legally use a radio which has been type-accepted for use on the marine bands.
In an extreme emergency, you can use any radio on any band to attract attention and get needed help.
Many sailors routinely use ham radios on the marine bands (illegally). They may or may not get away with it over time.