Picture two people who cannot reach each other. One has the power to decide; the other needs something and has no voice that will carry. Intercession is a third person walking into the space between them and speaking for the one with no voice. Nothing in the request is for the speaker. Both meanings of the word are this same picture — only the powerful side changes, from a person in authority to God.
From the word’s history
Latin intercessiō, from intercēdō: inter- 'between' + cēdō 'to go' — literally a going between, which is still exactly what the word does.
拉丁文 intercessiō 來自 intercēdō，由 inter-（在中間）加上 cēdō（走）組成，字面就是「走到中間去」。這條字根線索到今天還完全對得上：不管是向有權力的人說情，還是替別人向神祈求，動作都是走進中間替人開口。
Wiktionary entry 'intercession' in the supplied evidence packet (source_ref kaikki:3f6f69a190036ae4:1288284461:12240)
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