A ballad is mostly lyrical, its progression is slow and it generally tells a story using short stanzas. It's like a narrative poem or song. Some stanzas are usually repeated. The stanzas are preferably four line or quatrains and in iambic trimeter or tetrameter.
A sonnet is a 14 line poem. There are two main types or styles of sonnets - The Petrarchan and Shakespearean. The Petrarchan has one 8 line stanza or octave and one sestate or 6 line stanza. Shakespearean sonnets are divided as 4-4-4-2, that's three quatrains and a couplet. The rhyme patterns and syllables vary.