Just to be clear, whether the ship has a Starbucks store or not, you can get a French press pot of coffee with breakfast in the Haven.
In addition to that, the Haven bar has an espresso machine with Starbucks coffee, so in the Haven restaurant (or lounge, pool, bar, etc.) you can order an espresso, cappuccino, latte, or my favorite an espresso martini. Those will come from the Haven bar and are included in your Haven fare (martini depends on your drink package), not from the Starbucks store (if the ship has one) which requires payment or the Plus drink package.
The ships that have a Starbucks store have more options, not different options.