過 logs the experience (I have done it at some point); 了 reports a realized event (the action got done). 看過 = have seen it before; 看了 = watched it (this time).
V過1 is the experiential suffix on a verb; the standalone 過 verb means to pass or cross (過馬路). Same character, but here it rides a verb and carries no motion of its own.
wrong negator: 我不去過日本 → 我沒去過日本
object before 過: 我看這部電影過 → 我看過這部電影
dropping 過 under 沒: 我沒看這部電影 → 我沒看過這部電影
English present perfect ('have seen') covers both 過 and 了; learners reach for 了 when they mean lived experience, losing the 'ever, at some point' reading.