I found out that these two levels look the same, and I like seeing these types of remakes, where the level looks different but plays the same way.

Yes, one from the Genesis version of Lemmings and one from ONML. There are a bunch of these:
Taxing 13 "Walk through here but cautiously" = Crazy 1 "Quote: "That's a good level""
*Taxing 14 "Value each moment" = Crazy 3 "Many lemmings make level work"
*Taxing 17 "Lunch time" = Crazy 14 "Time waits for no Lemming"
Taxing 24 "Keep all enemies out." = Crazy 6 "The Stack" (the one pictured)
Taxing 25 "Watch right and left!" = Crazy 10 "ROCKY VI"
Mayhem 10 "Dangerous balcony" = Crazy 2 "Dolly Dimple"
Mayhem 28 "Leftovers are not always a waste" = Crazy 15 "Worra load of old blocks!"
Present 11 "Field athletics" = Crazy 5 "24-hour Lemathon"
Sunsoft 15 "Exodus!" = Crazy 7 "And now, the end is near...."
The two marked (*) are not exact and have easily noticeable gameplay differences. Taxing 13 is exact in terms of terrain (other than decorative terrain) but a gameplay difference arises anyway because the Genesis version doesn't allow RR changes while paused. I believe it can still be solved lose-1, though I don't know the details, but not 100% as the ONML level can.