Got two versions of each image from my camera: JPG and NEF. What is NEF?

NEF files will offer more scope for quality post processing Compared with jpeg. Provided you have the time.

Jpeg shooting offers the quickest in-camera results notably for sharing to the web and social media.

The JPEG files will have all sorts of auto corrections done by the camera - such as making grass greener, smoothing or sharpening, "fixing" exposure, all sorts of things which depend on he camera model and the settings in the camera. It's designed for consumers, so they get the best possible result without having to learn lots of technical stuff.

The NEF (or RAW) files are what the camera actually sees BEFORE it starts to correct and "improve". Professionals tend to want to work in RAW. It lets them use their skills they have practiced and studied for so long, to get exactly the picture they want, rather than the picture the camera maker thinks that consumers prefer. It means that you have to choose carefully what to do with the RAW file. It means you need a good computer monitor, properly set up to do your corrections, and the time to do them.

Only you know what kind of photographer you are, and want to be, and how much time you can afford to get the RAW stuff working, and how picky you are, and if the work is for other people, what they expect. Some photographers can control their set up precisely in the a well-lit studio where they can veto make-up and clothing selections, and others are trying to capture fleeting moments in challenging situations where every photo needs different correction. Some photographers take pride in delivering an "uncorrected" image straight from the camera, while to others that is unimaginable. It may also depend on other factors, like whether you have to deliver 500 pictures from a shoot, or just one perfect one.

Do not be so dismissive of the NEF, which is Nikon’s format for a “raw” file. While a raw file out of the camera  may not look as good as the jpg on your computer, a simple tweak will improve it so that the image quality equals or exceeds a jpg. (A jpeg is processed within the camera so that it improves upon the raw information recorded by the camera.)

In Elements, raw files are processed in a separate editor known as Adobe Camera Raw (ACR). I highly recommend that you take a look at it. ACR provides sliders to easily control all aspects of a photo’s exposure and color balance. Once the photo has been enhanced in ACR, it can be opened in the regular PSE Editor for further processing.

ACR can also be used to enhance jpeg files but if you have a camera that offers the capability to create a file with more information than a jpeg, why not use it? (Others may disagree with my last statement but if you are really interested in learning about NEF and raw files, take a look at the Google search provided by Peru Bob).

If if you don’t like having the duplicate jpg/NEF files showing in the Organizer, there is a setting in preferences that allows the auto stacking of the files.

The is a setting in your camera which allows you to choose to save as jpeg, NEF, or both.

See here:

What+is+NEF

Check your camera's user manual for detaiuls.