Actually Dm7 (D F A C) and F (F A C) would be closer to identical. Sorry to be a theory stickler...
And now that I think about it I believe that the jam actually uses a Dm7. I seem to remember that from the Anthology songbook. But essentially it's the same w/ the 7 or as a straight minor. Take it easy.
Don't be a poop.
I said twins. Not identical.
And yes, it is closer....
Kinda like Emaj7 & Abm a very common whip (Eyes, Cassidy)
BTW, I love theory and learning so thanks for reminding me of something I learned long ago and stored it away and did without thinking about it!