According to the novelization, R2-D2 was indeed with Chewbacca aboard the Falcon, so the first scene must have had some OTHER R2 astromech.
Each time, Chewbacca would wave.
Had he been equipped to do so, R2-D2 would have done likewise. -
[From the novelization]
scifi.stackexchange.com/users/976/DVK-on-Ahch-To
I could be wrong but I believe the character in the top image is shinier, newer (i.e. different) than the one in the bottom image.
During the film, I recall thinking that the character in the top image looked familiar, but couldn't be who you (and I) thought it was.
So the next image made sense to me.
I had the thought "Oh okay, must have been a different character."
scifi.stackexchange.com/users/23154/gary
Consider the placement of the individuals in the sending off scene.
Front and center are C-3PO and BB-8.
Off to the side (and behind another person) is an R2 unit.
One would expect, that if that was R2-D2, he would have been standing in close proximity to the two droids in the middle given R2-D2's importance.
That this expectation is not met indicates thats not R2-D2.
scifi.stackexchange.com/users/None/
No, they are patently not the same droids.
As you can see, the one that leaves the Falcon (pictured to the right below) has a blue top and white legs.
Presumably it's R2-D2.
The one on the flight apron (pictured to the left) has a grey top and a grey body with a white trim.
scifi.stackexchange.com/users/20774/Valorum
To me the droid looks more like R2-Q2 who was also in the Force Awakens action figure set.
scifi.stackexchange.com/users/64293/thomas
In this scene, we see...     R2-D2 waving goodbye to Rey and Chewie in the Falcon      But, here, in this next scene we see...    That R2 is there with Chewie in the Island     So, is it a big mistake in the movie??
Is this the same droid in two scenes from the Force Awakens?
scifi.stackexchange.com
<star-wars><the-force-awakens><character-identification>
scifi.stackexchange.com/questions/112545
scifi.stackexchange.com/users/35749/LcSalazar
No these are not the same droid. The droid that leaves on the Falcon appears to be R2-D2 whereas the droid in the other scene has a different appearance and is likely a different unit. The other droid is possibly R2-Q2. It must have been another droid that looked like R2-D2 - possibly R2-Q2 from The Force Awakens action set.
It must have been another droid that looked like R2-D2 - possibly R2-Q2 from The Force Awakens action set.