Chet -- who's moonlighted as a rapper/reggae artist in the past, and has a firm grasp on all things hip-hop -- shared a hilarious text message exchange with his movie star dad this week ... who was apparently uber-curious about the year's biggest moment in pop culture.

You can easily see Chet's inner rap nerd burst out explaining the beef with intense detail ... but he may have lost his pops along the way, especially based on how Tom responded.

In reply to Chet's very long text explaining the whole beef ... Tom wrote, "Holy cow! These are fighting words. People taking sides?? Who's winning??"

To that, Chet simply said ... "Did you not just read what I said" -- which seems to suggest to people Kendrick is winning/won, at least based on CH's interpretation of things. Like we said, he posted the entire exchange on his IG Story, and the internet is having a field day with it.

Of course ... the Hanks household is no stranger to hip-hop, even outside of Chet. As you may or may not know, Chet's mom (and Tom's wife) Rita Wilson is a big rap buff herself -- particularly when it comes to Naughty by Nature and their classic hit "Hip Hop Hooray."

In terms of the Kendrick-Drake beef ... it's all quiet on the war front right now, as it appears the saga has come and gone -- without any new barbs being thrown from either side.