Rearrange is used to say something like I am going to rearrange the fridge. Rearrange is used most of the time. The only time I use the word shuffle is when I am talking about shuffling a deck of cards or shuffling songs on my playlist.

It's not the same meaning. In general, rearrange is within your control, shuffle is out of your control. In general, if you rearrange something, you control how it will be arranged and if you shuffle something, you don't necessarily know how it will be arranged. We've got visitors coming soon and our conference room looks chaotic. Can you take care of it? I suppose I could rearrange a few things.