What is the difference between "Come on home" and "Come home"? In this case "Come on" is a phrasal verb?
Yes, I think come on is a phrasal verb, and a rather colloquial one. I'm finding it hard to define its meaning though. Sometimes it does mean the same as come, with a connotation of either annoyance or invitation (depending on the tone of voice). It can also have a much more abstract meaning, something like "I want you to do something, or finish something".
In this case, your two sentences do have the same meaning, but come on home is more friendly, either coaxing or inviting.
Come on home could be taken to imply that the person you're talking to is already on their way home, and you're welcoming them in advance.
Come home might be more of a request - this person isn't necessarily thinking about coming home and you're suggesting it in the hope they will.
These are the two meanings I would first assume if, for example, I overheard them on one end of a phone-call.