Just look at the pricing. $600 or less for a week-long cruise does not equate to premium. And Norm, interesting to note that it usually costs more to sail on a Voyager class ship for a week in the Caribbean than a Celebrity ship or HAL ship.
It depends what category of cabin you are able to book. Historically, cabins on cruise ships usually sell out from the bottom up and from the top down, converging in the middle -- but not always.
In any case, most markets exhibit some degree of overlap between a "premium" product and a "mainstream" product. Consider automobiles, for example -- a Mercury ("premium" brand) traditionally cost more than the equivalent Ford ("mainstream" brand), but the base model also had more standard features. If you load up the Ford with optons, OTOH, the price would go above that of the base Mercury by a significant amount.
It's the same way in cruising. An cabin on a "premium" ship usually will sell for more than an equivalent cabin on a "mainstream" ship, but the "come-on" prices that you see in advertisements are not necessarily for equivalent cabins. One might be for an inside cabin on a lower deck, while the other might be for a cabin on an upper deck. In fact the "premium" lines usually have a few bottom categories on which they don't offer early booking fares so that they remain open for "come-on" pricing -- but these cabins are so few that they sell out almost immediately when the "come-on" ads appear.