With fingerpicking, chord notes are played separately instead of simultaneously like with a pick. Patterns can differ both rhythmically and in the order of which fingers pluck which strings. The chords often (but not necessarily) involve string skipping, meaning they aren't always arpeggiated in ascending or descending order.
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In fingerstyle guitar, it’s common to have the thumb playing a bassline on the bottom strings while the remaining three fingers play chords or a melody line on the higher strings.