By the term fastest moving do you mean a speedy action movement or fast moving from one place to another?
If you're into a question about a fast movement of the whole body from one place to another then a Peregrine Falcon will be the winner. This kind of Falcon has a top speed of 390 km/hr on free falling.
Of course, a Marlin sailfish and cheetah are also there to compete. But when it comes to acceleration a cheetah will be far behind. Cheetah's acceleration is a bit lame and its top speed of 120 km/hr will be achieved only for one or two seconds. A marlin sailfish also has a peak speed of 110 km/hr but nowhere near to the falcon.
If you are asking about the fastest action by a creature then a termite can win any creature hands down. Ants are the next close to termites for their fastest movement.
Anyway, my vote is for ants
According to National Geographic, Acinonyx jubatus or commonly known as cheetahs are still considered as the fastest moving animal on earth. They can go from 0 to 60 miles an hour in just three seconds. Cheetahs have an average life span of 10-12 years and are typically found in the wild in the eastern and southwestern African regions. Unfortunately, populations of cheetahs are highly under pressure as the wide-open grasslands are continuously being degraded and converted into other land uses.
On the other hand, in marine ecosystems, sailfish are considered the fastest, which have been known to reach speed of about 60 mph when they breach the waves.
In another article, gyrfalcon named Kumpan was found to accelerate in speeds between approximately 116 - 129 mph after free-falling from a height of 500 meters.
By stating fastest moving creatures, I'll assume you're referring to all animals, be it land, air or sea animals. In saying so, it's really going to be difficult choosing a particular animal as the fastest.
Comparing the speed of one man to another is quiet understandable as all humans belong to the same group. But even the speed of a minor can't be compared with that of an adult. Hence, drawing a comparison between the speed of an ant with that of a mouse is way out of proportion. This is the reason why bringing together and considering different animal categories to get one compared result isn't possible. There's the difference in their nature, am talking about sizes and body, as well as the different animal groups they belong to.
However, there's a list of the fastest animals from the different categories they belong to. The fastest Land animal is Cheetah, with a recorded speed of 109.4 - 120.7 km/h.
The fastest animal in air is the Peregrine Falcon with a recorded diving speed of 389 km/h. This bird is largely classified as the fastest animal on the animal kingdom.
The fastest animal in water or sea will have to be the Black Marlin with a recorded speed of 129 km/h.