I seem to hear 准备 and 预备 used for “prepare” and not as often to mean “plan".

我们准备搬到美国； emphasizing the need for specific preparations for the move.

Myself， I use 计划 or 打算 for planning something.

我们打算看新的电影； emphasis on merely being a future plan。

What are the differences in usage between 准备 and 预备？ At what point can one not use these to mean ”plan“？