A believer can be pictured as the person standing behind an idea. Someone asks, does this hold? and this person says yes, and lives as if it does. The word points at the person, not at the idea, and it does not say how loud they are. Whether the idea is a faith or just a habit that works, the picture is the same: one person, one thing they stand behind.
From the word’s history
The packet's Wiktionary etymology traces believe to Old English belīefan; believer is that verb plus -er, the ending that turns an action into the person doing it, as in teacher or writer.
來源的字源樹把 believe 追到古英語的 belīefan。believer 就是這個動詞加上 -er，而 -er 做的事跟 teacher、writer 一樣：把一個動作變成做這個動作的人。所以字面上它就是「相信的那一個」。
packet Wiktionary etymology_text for believer (kaikki:3f6f69a190036ae4:791017648): Old English belīefan > Middle English bileven > English believe, with the agent suffix.