It's all about subject distance
Stop talking about lens width, or which lens width you prefer. Those are crops.
Those different crops affect the way photographers approach subjects, and the subject-background ratio. They give different looks, but it's all subject distance.
Ansel Adams in 'The Camera':
"...the effect of changing to a lens of longer focal length is to increase the size of the image of any part of the subject. Beginning photographers therefore often assume that the effect of changing to a longer focal length lens is equivalent to moving closer to the subject. In fact there are important differences. Since photographers often do both at the same time- change lenses and subject distance simultaneously- the effects of these two acts are often confused.""
So what does subject distance actually do?
Understanding Subject Distance
When I say "subject distance" I mean the distance between the camera and what it is taking photos of.
What I actually mean is the relative distances of everything in the scene.
Basically, because of perspective, things that are further away are smaller. When we have photos with multiple objects at different distances (ie: the subject and the background), we can affect the percieved relative sizes of these objects just by moving closer or further away.
For the curious, there are special lens, telecentric or "orthographic" lenses, that do not experience perspective distortion.
First, watch this video.
In the dolly zoom, also called the hitchcock zoom, the cinemetographer is moving the camera forwards and backwards. They are also zooming in and out at such a rate that the subject stays in the same relative location.
It's All Relative
If I am 5 unit's from the camera and the background is 10 units from the camera, 5 unit behind me, the background is twice as far from the camera as it is from me.
So the background is pretty big, all things considered.
If I walk towards the camera so I am only 1 unit from the camera, but the background is still 10 units from the camera, now I am 10 times closer to the camera than the background. Before I was twice as close.
I am going to be 10 times bigger than the background, while before I was only twice the size. I am going to take up a lot more space in the frame! You will see less of me, or more of the background.
What Now? Math is confusing!
Relax. Just think about the relative distances to the camera everything is. Not actual feet or real life units, just how many times closer to the camera different objects are.
Lets think back to the hitchcock zoom video above ('History of the Dolley Zoom'). Consider one of the shots, from jaws.
The top image, the cameras is far away. The bottom image, the camera is close.
Relatively, the background is much closer to the camera, compared to the actor, in the top photo than the bottom photo. The actor is much closer to the camera than the background in the second photo.
In the bottom image, we can see the orange/white striped building that we couldn't see at the beginning of the shot. When the camera got closer to the actor, it also zoomed out (so the actor stayed the same size), revealing more of the background.
More Than Just A Film Gimmick
The hitchcock zoom, in film, is just demonstrating the optical effect. How far away to stand is, almost always, the first decision that photographers have to make.
How do you learn this? I can show you a million photos, or you can take photos of the same object while moving forwards and backwards from it.
Zoom lenses just crop
When you zoom in or out with a zoom lens (or by switching lenses), Nothing about the image changes. Nothing except for what section is visible, it's just a crop!
Okay, the depth of field changes. Wider lens = deeper depth of field. Nothing changes about the nature of the size of the objects in a scene. They don't really "get bigger", that only happens when you move closer. All you are doing, when you zoom, is crop the photo! That's it! That's it! Nothing else!
Move your feet to actually, you know, change the image being taken.
“If your pictures aren’t good enough, you’re not close enough.” - Robert Capa.
Stop zooming in to get closer. Start moving your feet. Making the subject larger than other object in the frame doesn't just clearly signify it as more important. It also gives a more intimate feeling, more involved. Exaggerating object sizes to be larger than real life (compared to background) is much more interesting than a photo that puts the audience further than they normally are. Bring the audience closer than they are used to!
This is just a guideline. When starting out with photography, I highly encourage you follow it. Start moving your feet while you take photos, and see how they change.