Merick's comment does make it seem like there is a difference between a "Spaceship" and a "Starship." While it may be a matter of quality over quantity, it still lends support to the idea that 23rd century nomenclature makes a distinct difference between the two.
Which tends to support what I'm saying. For a time during the 23rd century a starship was seen as something special.
It's kind of like saying, "Now that's a real
car rather than just a convenience on wheels."