The terms are the same basically as laymen. Incapacitated means physically not capable. Incompetent lacks the mental competency or mentally disturbed as to affect their ability to think rationally.
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This is a very broad question and unfortunately there has not been enough information provided to answer your question. I suggest you contact a Probate litigator who is experienced in conservatorships and litigation.
No legal representation exists by virtue of this answer. It is recommended that you contact an attorney directly for a more complete response.