Design is a HUGE concept that encompasses user experience, usability, visual appearance, and much more. Usability is exactly what it sounds like: how usable your product or service is. Good design and usability definitely go hand in hand, but an attractive design is not necessarily the most usable.
Take architecture websites for example. These are often minimalistic and appeal to their audience's aesthetic, but unobtrusive calls to action and respect for whitespace don't necessarily create the most usable experiences.
Designing for a great experience can also mean breaking conventions, which can also negatively impact usability for new users. Familiar patterns are usually more usable because people don't have to think, but creating appropriate challenges for an audience may lead to a more rewarding experience in the long run. Take gmail's use of tags instead of folders for example.
As always, the key to finding the right design is to understand your stakeholders and their objectives for the project.
To get back to the detail of your question though, it sounds like it's more a matter of what point in the process it happens. Usability refinement is usually based on testing of a working site or prototype, so I'd organize my services by the stage of the process they occur.
For example (roughly):
- ideation / sketching
- prototyping / WFs
- usability testing (repeat 1-3 as needed)
- visual design