The triads are all agreements of three sounds, whether doubled or not.
Triads in fifths: the perfect major chord and the perfect minor chord.
Triads with altered fifths: the diminished chord and the augmented chord .
Triad consists of a stack of two major third and / or minor. The fundamental and/or fifths can sometimes be doubled. The absence of the fifth example right hand on the piano is also possible, especially if the pianist is accompanied by a bassist.
Often considered in jazz as a "poor"chord in harmony for the period of bebop the triad is abandoned in favor of seventh chords harmonically rich. But the triads found a renewed interest in contemporary music, contemporary jazz ... (stacking triads,triad on bass ...)