The parts do the work here: petition plus -er, the one who asks, with petition going back to Latin peto, to ask or seek. So picture someone standing in front of whoever has the power to decide, holding a written request. The two meanings differ only in who is standing opposite - an office or a court - and in both, this is the side that asks, never the side that decides.
From the word’s history
From petition plus the -er ending that names the person who does something; petition itself goes back through Old French to Latin petitionem, from peto, to ask or seek. The modern picture is still exactly that: the one who asks.
由 petition 加上 -er（做這件事的人）組成；petition 再往回是拉丁文 petītiōnem，來自 petō「要求、尋求」。今天的畫面沒有走遠：就是「開口要求的那個人」。
Wiktionary entry for 'petitioner' (noun), etymology_text supplied in the evidence packet: 'From petition + -er', with the tree Latin petō > petītiōnem > Old French peticiun > English petition.
登入就可以看每一支怎麼連回核心畫面。