Is there a difference between a sermon and a homily?

A homily is shorter and less formal.

A homily is a type of Sermon that explains scripture.

When I was in seminary, I was taught that a homily is sermon based on a specific passage of scripture, usually the passage read as part of the same service. A sermon is more general, and may be based upon scripture, doctrine, or teachings.

One of the more unnoticed changes in the Catholic Church after Vatican II was an encouragement to use homilies during the Sunday Mass.