The difference between triads and arpeggios is that a triad consists of three notes, while an arpeggio is a chord played in broken intervals. Triads are the most common chords in music because they can be formed from any combination of notes. For example, if you take a C major triad (C-E-G), the notes can be arranged in any order and still form a C major triad.
This flexibility makes it easy to see how so many songs use the same chords repeatedly. Arpeggios are similar to triads, but they have more than one note per chord instead of just one note repeated three times. The word "arpeggio" comes from the Italian word arpeggiare ("to play on a harp").