Depends on your philosophical outlook. https://en.wikipedia.org/wiki/Ship_of_Theseus
In this instance, are both "det's" pronounced the same?
"Is it the same boat" should be accepted, no?
A boat (båd) is usually quite different to a ship (skib) in, for example, size. But it doesn't really hurt and Danes will know what you mean.
By English nautical convention does a skib have one or more båd on board
Hell yeah, make sure you board the same skib!