Hello! This is an interesting debate/discussion I have seen some users on here contemplate before, so I figured I might as well do the same. I was thinking about it earlier today, and think I came up with an answer, at least for myself.
Meaningful: Personally, I think all songs are meaningful. I know it sounds crazy but hear me out first. Most songs (that I know of anyway) have some sort of message. Something that they want the listener to know. It could be a love story, going through hard times, advice, enjoying your youth, how much taxes suck, why a monkey is red (blame Hyuna, not me) or anything else. If the artist didn't want to convey a message, they wouldn't use words. Even that isn't entirely true because some songs may still have some sort of message and no lyrics, who knows?
I think any song containing any message has meaning. Now, whether or not the listener likes the message will vary from listener to listener, but it still has some inherent meaning regardless, thus making the song meaningful, at least by my approach. Also, some songs may have more meaning than others, depending on how effectively/well the message is conveyed in the song through various ways (the beat, vocals and melody, for example). Even songs like "Ping Pong" by Hyuna and Dawn or "Hey Tayo" by Enhypen, as silly as they are, have meaning and are meaningful.
Deep: I consider a song to be deep if it meets two criteria: 1) the message of the song is one that many listeners can relate to and 2) the message of the song is described in a particularly accurate or especially vulnerable way from the artist, going above and beyond what most pop songs discuss in terms of lyric quality (not to insinuate that all pop songs are evil and bad or always have shallow, surface level lyrics, but you get my point). Extra points are awarded if the song has more than one interpretation/meaning or the beat contributes to the depth of the song, but those are not concrete requirements in order for me to consider a song "deep".
I hope my explanations and distinctions between the two made sense. By my definitions, a song can be both meaningful and deep, or just meaningful, but it can't be deep unless it is meaningful first. Anyway, what do you guys think is the difference between a "deep" song and a "meaningful" song? Feel free to provide examples if you wish, but you do not have to, since I didn't really. Don't fight over definitions/examples and stay calm and mature about this discussion. I'd love to hear what you think, as well as if you agree or disagree with my stance. Have a great day/night!