The difference between a lyrical poem and a sonnet is a sonnet consists of only fourteen lines. The particular lines rhyme to only a certain scheme, while on the other hand a lyrical poem is quite different. A lyrical poem expresses thoughts and feelings in a song-like style. They are alike because they both have rhyme and rhythm towards a certain subject. They are different because they have complete different number of lines.
The poet would choose a sonnet to capture the readers, almost like a riddle, and get them interested in the way the poem is designed. On the other hand, a poet would chose the less strict lyrical poem to take the reader on more of an emotional heartfelt story.