So each stanza contains 20 syllables times 3 stanzas equals 60 syllables total. Since there are 60 seconds in a minute, I'm going to go out on a limb and proclaim that's the origin of the name minute poem.
Rispetto #1: Poem comprised of two quatrains written in iambic (unstress, stress) tetrameter (four feet--or, in this case, 8 syllables).
Rispetto #2: Poem (or song) comprised of 8 hendecasyllabic (11-syllable) lines--usually one stanza.
Both versions appear to follow this rhyme scheme: ababccdd (though I also found a mention of an abababcc pattern). Plus, I found more than a few sources which claim rispettos were originally written to pay "respect" to a woman.