There are really two separate issues at play here.
First if all, just looking at something through binoculars or a telephoto lens will make it look bigger, because the lens physically magnifies the image.
But second, looking through a telescope or a long lens at a distant object when there are also other more nearby objects within the frame can give a distorted impression of size.
The classic example is telephoto shots of the moon. Here is an extreme example, which is a screenshot from a video.
External Quote:
Using lens compression to capture a giant moon is nothing new, but photographer
Daniel López has taken things to a whole level. He set up an
ultra-telephoto lens about 10 miles (16km) away from a volcano and captured this mind-blowing 2-minute video that shows a moonset
in real-time.
López shot the footage near Mount Teide in the Canary Islands off the coast of Africa. He used a giant telescopic lens, Canon teleconverters, and a Sony a6300 camera.
Source:
https://petapixel.com/2018/06/05/this-is-what-a-moonset-looks-like-with-an-ultra-telephoto-lens/
So here, the moon is 230,000 miles away and the people on top of the volcano are 10 miles away.
Ratio is 10 miles to 230,000 miles =
1:23,000.
Whereas in a photo like this with a wide-angle lens, the person might be (at a guess) only six feet away, but the moon is still 230,000 miles away.
Ratio is now 6 feet to 230,000 miles =
1:202,400,000
So the moon will appear 202,400,000 / 23,000 = 8,800 times bigger in the telephoto image than in the wide-angle image, relative to the people. Obviously in this case the people are also smaller in the frame, so the moon size itself will be proportionally slightly less enormous, but if you blew it up even more so the people were as tall as the person in the portrait, that's how much bigger it would be.