These three terms have a place in the process of Interior Design. Re-Design, Re-Style and Re-Model.
In the Interior Design sense, Re-Styling means to keep what you have, but reshape, resize, recover, repaint or add to. There are no structural change.
Re-Design is similar to Re-Styling, however, it also can involve new surfaces on walls, floors, and Window Treatments. It also can involve adding new accessories. It can involve minor structrial changes.
To Re-Model is to take apart and renew. It will usually involve repainting, resurfacing combined with structural change. It is to renew parts of old structure and bring it up to date.
New cabinets or cabinets resurfaced, new counter tops and door and drawer pulls and handles, new flooring, remove or add a wall, change the configuration of the bath or kitchen, enlarge rooms, install skylights are a few examples of Re-Modeling.