Reassignment to a vacant position is simply what it says: putting the disabled employee into a position within the company that already exists, but for which there is no employee presently assigned. Generally, it will be a position whose essential functions are capable of being performed by the employee with or without accommodations for the employee's restrictions. While the reassignment might mean the employee has a different supervisor, that is not necessarily going to be the case. The reassignment, might be to an open position under the same supervisor.
Changing the supervisor is just that - either moving the supervisor to another position, or moving the employee under another supervisor. It is very different in concept.
Do not get caught up with what the ADA says if you are a California employee. The ADA and its regulations promulgated by the EEOC are helpful but not dispositive. The FEHA and the regulations promulgated by the DFEH should be what you proceed under.
Good luck to you.
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Under ADA and FEHA (the more important law than ADA for your purposes), an employer doesn't have to provide a perfect accommodation or an accommodation that you want; it only has to be "reasonable." There is no bright line rule as to which accommodation is reasonable, and it should determined through a flexible discussion or "interactive process."
To elaborate a bit on Mr. Pedersen's excellent answer, "FEHA" stands for the California Fair Employment and Housing Act, California Government Code sections 12900, et seq. (FEHA). As Mr. Pedersen indicated, the FEHA is more favorable for employees than the ADA. You can see this for yourself by reviewing two documents:
Please look at my Avvo guide on the ADA: http://www.avvo.com/pages/show?category_id=6&permalink=disability-discrimination-in-employment.
Please look at my Avvo guide to the differences between the ADA and California's more generous FEHA: http://www.avvo.com/legal-guides/ugc/employment-disability-protection-under-californias-fair-employment-and-housing-act-and-federal-ada?published=true.
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