Some people like to work from home. This is specially true of some professions like photographers or recording artists. For these professionals, they usually have a back-up at home. Though usually these professionals have their own home studios, the equipment in these studios are a bit less in than those in their work studios. For a photographer, there might be less lighting equipment, and for a sound editor, a less powerful mixer and speakers.
The whole point of the home studio equipment is to allow the professional to work at peace. The available equipment at the home studio would be less powerful or industrial-strength, as it were, but fully functional to do the work. Of course for the highest paid professionals, the home studio equipment is no different than those found in professional studios, just bought out of the pocket of the photographer or sound editor or disk jockey.
Suffice to say, it is only the budget which differentiates the home studio equipment from a professional studio. Besides that the work would still be the same quality as it is done by the same person.