Even though I played the flute for a whopping two years of elementary school, I wouldn't exactly call myself an expert on music theory.
I had to Google "melody vs. chord progression" to better understand the Thinking Out Loud vs. Let's Get It On lawsuit. The simplest explanation I found was that if someone asks you to hum a song, you're going to start humming the melody, not the chords. But, since my brain operates best in metaphors, I had to come up with a few to fully wrap my head around the concepts.
(Beware, I am most certainly oversimplifying this stuff.)
So here's what I've got: the chord progression is like the stage setting, the lyrics are like the dancer, and the melody is like the choreography. You can't steal the dancer's identity--it is the most unique element of the show (and, duh, identity theft is illegal). You also can't steal the choreography of the dance because choreography is protected by copyright. But, you can perform your own dance with your own choreography on the same stage (maybe the set looks a bit different, but it's the same stage).
Or, here's another one: the chord progression is like a combination of colors--let's say, red, orange, yellow, and pink--and the melody is like the sunset that you'd paint with those colors. (I'm not sure how the lyrics would fit into this metaphor, but, bear with me... maybe this one only works for the instrumental version.) In this lawsuit, Ed Townsend's heirs seemed to be saying: "hey! you can't also use those 4 colors to paint a sunset!" or "hey! you can't also perform your dance on that stage!"
I think Sheeran won this case not by delving into the nitty-gritty of music theory and copyright law, but by appealing to the jury's common sense. He won by arguing that if he were found guilty of stealing, then dozens (if not hundreds or thousands) of other songs and artists would be guilty, too. As one wise reddit user on this thread puts it: "Everything is derivative of something. That has been true since the second cave drawing."
In a recent interview with Howard Stern, Sheeran explains how he brought his guitar into the courtroom to prove this to the jury, and in the NYT article that ran after the verdict was announced, Sheeran is quoted as follows:
“We have spent the last eight years talking about two songs with dramatically different lyrics, melodies and four chords which are also different and used by songwriters every day, all over the world,” Mr. Sheeran continued. “These chords are common building blocks which were used to create music long before ‘Let’s Get It On’ was written and will be used to make music long after we are all gone.”
Alas, after reading up on all of this, I'm still no expert on music theory, and it's a shame that the juries in these trials can not be made up of experts. But it does seem like this particular jury made the right decision. In conclusion (and with credit to one of the top reader comments on the NYT article), I give you... The Axis of Awesome.