Mother 1 + 2 is a compilation containing remakes of Mother and Mother 2.

Differences

Mother

The censorship of the American prototype was added. That means no blood, crosses, or tobacco.
A run feature was added by pressing R.
Talking and checking can be executed by pressing L.
The screen animates when a melody is learned.
PSI is learned in a different order.
Your dad doesn't tell you to hold reset when you save and quit.
A sleep mode was added.
Movement is more fluid.
There's a mosaic effect when you enter battle.
There's no "map" item.
Battle text speed can be changed.
Enemies can be checked.
SMAAAASH! is always displayed in green.
Text changes color depending on the player's condition.
The strip club has become a shop.
The "Repel Ring" has been added.
The path to Magicant is different.
The "Friendship Ring" is gone.
The reference to Dragon Warrior has been removed.
Check will tell you if you might be attacked.
A scene showing everyone escaping Eve's factory was added.

A bug that allowed the player to use the Exit Mouse in the Cave of the Past was fixed.
The Shattered Men in Summers Museum disappear when Giygas is defeated.
Several songs sound slightly different.

Mother 1 + 2 was popular enough in Japan that it was rereleased as a Nintendo "Value Selection" game.