De website Petapixel.com published an interesting article about the difference or zooming with your feet and with a lens. 

Below is a video (you can see it also on Petapixel), and I recommend that you watch it. 

(photos and article from Petapixel.com)

Another very interesting image. This GIF animation below was in the comments on this article in Petapixel.  

The commenter wrote this: “I’m teaching my photo 1-2 students this concept right now. They had to pick an object and take 7 photos of it at 7 different focal lengths, but keep the object the same size in the photos. Then use photoshop to make the photos into an animated gif. Like this:

I tell my students that if they want to be complete photographers they have to understand the impact that focal length will have on the background and use it to their advantage.

This is an amazing gif and you can see the differences between using different focal lengths. 

I think a lot of photographers can do their advantage with.