Nightmare and Dream were constantly as each other's throats. And Nightmare was tired of Dream Blaming him for everything, so Nightmare made a bet with Dream. They'd use a certain artifact to reset the Multiverse with the two of them Reversing Roles. Nightmare becoming the Guardian of Positivity and Dream the Guardian of Negativity. So he could see just how bad Nightmare had it back when the villagers came originally.

Nightmare is Taller and more Masculine due to a number of factors. Mostly due him being 500 years older before the Reset. Dream is smaller, more petite, and FUCKIN ADORABLE. And for some reason. . . they are very Flirty. Likely due to living with Ink, Blue, and Lust for so long before the Reset.

They don't remember much of their past lives, the memories they do have come in dreams. Nightmare is insanely protective of Dream due to the past Nightmare's feelings of regret, guilty, loneliness and bitterness. And Dream is a f**king Bro-con and acts like a freaking anime character about it.
And when I say Nightmare is overprotective, I mean it's to the point he won't let Dream walk around on his own. . . as in he Carries Dream like a toddler everywhere when the two leave their castle.