My camera (fujifilm F810) does an 8 megapixel shot but I can up that again to a 14 effective megapixel shot.

What is the difference between the two?

Interpolation.

Extra information (pixels) are calculated from surrounding pixels.

A little unfair practice in this camera is the compression of the final picture. A much higher compression is used on the lower resolution pictures giving a lower end quality than it should. On top of that the higher resolution has a lower compression. The difference between the two resolutions are much higher because of this "trick".

If you shoot a native resolution picture, calculate the extra pixels through interpolation and store it in a LOW compression format the result will always be beter than shooting a picture at native resolution and store it with a HIGH compression.

http://www.dpreview.com/reviews/fujifilmf810/page8.asp

You can find a comparison between a 12Mb (interpolation) picture and a native 8Mb. My personal opinion is that the 8Mb picture is of much better quality.

My camera (fujifilm F810) does an 8 megapixel shot but I can up that again to a 14 effective megapixel shot.

What is the difference between the two?

So in conclusion, when you buy a camera, make sure to see the effective resolution (real sensor's resolution) than advertised maximum resolution (interpolated). Similar to optical zoom (real lens zoom) than digital zoom (interpolated).