So I think the best way I can explain it is that each of the three words have slightly different nuances, but almost the same exact meaning. In most situations you can use any of these options to accomplish the same intent. I hope the below examples help, but let me know if you want more.
"The message comes off as funny" - The message was received or interpreted as being funny
"The message happens to be funny" - The message was unexpectedly funny by chance
"The message occurred to be funny" - As a fact, the message was funny