Not really. Generally a petitioner or respondent is the terminology used for a "petition" such as a petition for receivership, petition for dissolution of marriage, or administrative proceedings. A plaintiff and defendant designation are used for most civil actions and the lawsuit is called a Complaint rather than a Petition.
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The words defendant and respondent are often used as synonyms. It is similar for Plaintiff and Petitioner. Certain courts utilize one or the other but when people mix them up its not unusual and doesn't invalidate anything.
I would not use that terminology in that situation, but I would not consider it important. Most judges are smart enough to put substance over form. Unless the attorney is using that term because of your status in some other proceeding, I would probably regard it as an unimportant error.
You can get a free article on small claims procedure here: www.DisputeResolutionFL.com
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Best wishes for a just and expeditious resolution.