Usually you walk straight home from school. But today you take a detour to buy some candy on the way home. Which will
change, the distance of our walk home, the displacement of
your walk home, or both?

the distance of our walk home.

Explanation:

In Physics when we speak of distance we refer to the space traveled that is always measured on the trajectory, while displacement refers to the space from an initial position to a final position regardless of the path. When the path is a straight line, the space traveled is equal to the module of the displacement.