Positional Awareness
Actually, 2 bytes

10


Try it online!

This prints

0
1


while the (only) other permutation

01


prints

1
0


How it works

In Actually, consecutive digits are parsed separately, so 10 pushes 1 on the stack, then 0 on top of it.

When the program finishes, the stack is printed top to bottom, so it prints 0 first, then a linefeed, then 1.

The derranged program 01 does the same, in the opposite order.