What is the difference between a focal length of 35mm and 50 mm on a DSLR lens?

Looking at these two lenses:

AF-S DX NIKKOR
35mm f/1.8G

and the

AF NIKKOR 50mm f/1.8D

The aperture on both lenses are the same but I was wondering what the difference in effect will be on the images due to the different focal lengths?

How will each focal length effect the end result?

Added (1). Just to clarify, I'm trying to think which would be the better buy.

Another question I have would be, will having one focal length allow me to achieve what I could with the other by just moving closer or further away from my subject?

Added (2). The camera I plan to use these lenses is the Nikon D3100.

And my purpose for wanting one of these lenses is for a greater depth of field effect.
I feel like the subjects of my pictures will be evenly distributed between objects and people.

For example, I may want to blur the background while taking a close up picture of a flower. Will I be able to achieve this with one of these lenses?
This is what I'm aiming for:

or

Another example of the type of picture I would want is of a person with a blurred background. For example:

or

the last image was actually from the 35mm sample pictures on the Nikon page but would I be ab

Added (3). (cut off from last detail)*

the last image was actually from the 35mm sample pictures on the Nikon page but would I be able get this type of effect with the 50 mm?

The 35mm is a little bit wider angle of view than the 50mm.

And that's basically it.

See how the 50mm is just slightly more telephoto:

Which one to get?
-That depends on what you are planning on shooting.

And the focal length difference is minimal, but yes, you could just take a step closer, but you want some breathing room between you and a model if you are shooting portraits. The longer focal length also gives you better depth of field, and less distortion.

This is a dramatic example of the depth of field relation with focal length:

To me these are different lenses for different purposes. I use my 35mm/1.8 for generic low light purposes. The 50mm/1.8 is a very good portrait lens, for which the 35mm one would be too wide, causing an unfavorable perspective if one gets close enough to avoid excessive cropping.

What camera do you intend to use it on? Be aware that the 50mm/1.8D won't autofocus on the D3000, D3100 and D5000, D40(x) and D60.

Edit:
That would be called shallow depth of field, not greater depth of field. Great depth of field would be understood to mean that lots of the image is in focus, not just selected parts.

Yes, the 50mm one would give you even more of such an effect. You get shallower depth of field by the following:
- opening the aperture
- longer focal length
- shorter subject distance

The 50mm one has a longer focal length, so it would give you a shallower depth of field than the 35mm one.
But again, the 50mm/1.8D won't autofocus on your camera. You would have to get at least the 50mm/1.4G (which will allow even shallower DoF due to f/1.4 instead of f/1.8).It has to be the G version, as that's a AF-S one, so it will autofocus on your camera. The D version of both the 50mm/1.8 and 1.4 is only AF, so it won't autofocus on your D3100.