Originally Posted by r31ncarnat3d
This is a bit of a tricky question...
For the simple part: Yes your subject will be closer/take up more of the picture the higher the focal length is. Using your example, a 300mm focal length will put the deer much closer/have the deer take up a larger part of the photo than it would at 250mm.
For the tricky part: Unfortunately "detail" depends on much more than the focal length. How much detail is resolved depends on the camera sensor (although all DSLRs these days are good enough to resolve things in great detail) and the optical quality of the lens. There are some lenses that can zoom in close to a subject and have fantastic optical quality and can resolve the smallest details (the 70-200 f/2.8L has been a want of mine for a while now), whereas other lenses use inferior optics that, while have a long focal length and can zoom in more, have craptacular image quality because the optics can't resolve details well.
+1 to this.
I'll also add that while longer focal length does mean shooting objects further away, it will also changes the composure significantly.
Meaning... if you position yourself close to the subject and shoot with a 24mm lens, then move way back and shoot the person with a 300mm lens the photos will look different even if all other aspects remain unchanged.
Longer focal lengths like the 300mm will make objects in the foreground and background look bigger. IE. You will only see part of the building behind your subject.
Short focal length like 24mm will make objects in the foreground and background look smaller. IE. You will see the entire building.
This is why the 50mm prime lens is many photographers lens of choice because it's results mimic the human eye. IE. the buildings on the skyline behind your subject will be the same size as what you see.