Neat Image is a filter designed to reduce visible noise and grain in photographic images produced by digital cameras and scanners. Neat Image is indispensable in low-light (indoors, night, astro) and high-speed (sport, action) photography. It is a tool for both professional photographers and digital image processing enthusiasts.
ISO, in the good old days, related to the sensitivity of the film and had a number 25, 64, 100, 125, 200, 400, etc.
A low number means low sensitivity, i.e. a longer exposure for a given light level. A high number is the reverse, short exposures at a certain light level.
In films the light during exposure caused a chemical reaction in the film that led to the deposition of silver or other molecules that were the black and white or colour in the negative/slide.
Slower films had much finer grain structure than faster films... imagine that more light hitting the film means that more molecules are likely to react to the light. With short exposures, less light means that fewer molecules are less likely to react equally so a more grainy image is produced. Light is a series of distinct protons and a certain number are needed to give the right light levels in a photo.
In a digital camera, the film is replaced by a CCD or CMOS sensing element that consists of an array of millions of light detectors - that give the pixels in your jpeg file. Again these are sensitive to light and the amount of light hitting them triggers an electronic response that is saved electronically as an analog voltage that's then converted to a digital number to be saved in the file on your card.
In the digital camera, however, there is only one CCD element, and ISO is an artificial change. What the setting does is change the sensitivity of the CCD by allowing it to be triggered by less light, but this still means that with short exposures each pixel is hit with less light, and relatively different light levels give a bigger difference (due to the higher sensitivity) leading to what appears as a grainier image.
In your camera it's pretty clear that 200ISO gives grainy images so you'd be better off at 100ISO. Also check the exposure compensation (read the manual). Some people here find that what the camera thinks the exposure should be and what looks right are different so you may need to underexpose the photo or overexpose it. In addition, different parts of an image have different "best" exposure times - a white plane will need a different exposure time from the darker background (to look right) and you need to get the exposure more right for the aircraft.
Get out there and experiment.... use a static aircraft and try a range of exposures and see what the difference is. Best way to learn.