There is always more than one correct way to design something. In our case, we make Web software, and our story owners can decide if they want a prototype process or a mockup process.
Prototype process: The developer creates a prototype and works on it until we know we have the right functionality, then we ask a designer to make it look good.
Mockup process: We start by creating a nice design and an HTML mockup, then ask a programmer to implement it.
I recommend choosing the process that looks easiest. If you are developer, start with a prototype. If you are designer, start with a mockup. If you are a product manager, a marketer, or a guest, start with the easiest next step.
However, there are two reasons you might make the choice based on the feature. If the feature requires a significant architecture, start with a prototype. If the feature has a big user interface, start with a mockup.