Your Nikon S6000 has a sensor that is capable of "seeing" 4320x3240 dots. Multiply that out, and you get just under 14 million dots in a picture. That's where the 14 megapixels comes in. In computer and electronic terms, pixels are used to refer to display or image capabilities. Megabytes are used to refer to storage space used.
Since each pixel can represent a single color out of millions of possible colors, it would not be practical to store and use digital images without some other intervening technology. Enter JPEG, the most common image compression technology in consumer cameras (and in images you see when browsing sites on the web). JPEG is an image compression technology that allows the picture captured by the camera's sensor to be represented fairly closely and faithfully but using less storage space. The compression algorithm finds patterns in the image and identifies ways to represent them using less data. In very simplistic terms that don't actually represent how JPEG works, think of this as an example: "Here's a big chunk of black in the picture." Rather than describe that as a color for each individual pixel, the algorithm can describe the area or region mathematically using substantially less data.
Now, here's where things get interesting. Compressing an image using JPEG causes original quality data for that image to be "lost". You may have heard the term "lossy" compression. That means that each time a JPEG image is modified, the quality of the image degrades at least slightly (and sometimes substantially). Further, the amount of storage (bytes or megabytes) needed to describe the image can actually increase. That is why, in general, you will see the recommendation that JPEG images not be repeatedly edited.
Another interesting effect of JPEG compression is that the "quality level" can be controlled and adjusted. A user might select a lower-quality level sufficient for their needs in order to maximize compression and minimize storage space. If, for example, you never had any intention of printing one of your photos, you could reduce the pixel count and quality level of the image and potentially save 50-90% of the storage space required yet still have an image of high-enough quality for display purposes (such as a web page).
What this means in practical terms is that there is great flexibility in how a JPEG image is saved and the software within one camera may have different settings than another camera. Also, the quality of the original image will affect the file size of the compressed image. A "noisy" original is more difficult to compress (or, more accurately, we would say that it doesn't compress as well). If your older Kodak camera's sensor produced more "noise" than your Nikon S6000, the file size of the Kodak's images could be larger, even though it's megapixel count was larger and even (particularly) if the images were not as good quality as the Nikon's.
If you want the best quality images possible, and don't care about disk storage requirements, make sure your camera is set to take the 14MP (megapixel) images. Some cameras also have the capability of saving images in RAW mode. This is a format that hasn't been compressed with JPEG and preserves as much of the original image quality "seen" by the camera's sensor as is possible in a consumer-level camera. This raw-mode image can be edited with image-editing software and copies can be saved in JPEG format (or other formats as needed), in sizes as desired.
Here are some other helpful tips for getting the best image quality from your camera:
Avoid shooting images in a high ISO mode. A rule of thumb for most digital cameras is that the highest ISO setting should be avoided at all costs, with the exception of not otherwise being able to take a picture. The next-highest setting should generally be avoided as well. Again, there are some cameras that do better than others, but this rule applies almost all of the time.
Particularly in low-cost consumer-level cameras, avoid using the most extreme end of the lens (zoomed in). The lenses usually have a softer image and tend to display image distortion. As an example, zoom into an image with horizontal and vertical lines and notice how the lines bend or arc toward the corners of the image.
Eliminate shake as much as possible. Even in cameras with image stabilization, the less shake, the better. This means avoid the slowest shutter speeds whenever possible. Use a tripod when conditions require (even a small table-top tripod works). Press the "fire" button gently. If your camera supports it (and I believe your Nikon does), use the short self-timer (usually 2 seconds). This allows you to press the button to take the picture, then steady the camera once again before the picture is taken.
While some of this response went beyond your initial question, I hope you've found the information helpful. Happy picture taking!
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