Simply, has several meanings:
1. [common] to firmly (mis)believe; to to make a (wrong) assumption
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2. [uncommon] (≒) to resolve; to make up one's mind
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3. [rare/obsolete] (≒) to think hard; to worry deeply; to be obsessed
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says can mean "firm resolution", but at least in modern Japanese, almost never means that. Today is almost always the nominalized version of 1., i.e., "(wrong) assumption". is a negative phrase that refers to someone who easily jumps to a wrong conclusion rather than someone who is determined. While / tends to refer to casual ones that can be corrected easily, an is often hard to amend by words.