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It is an excellent question that you ask, but kidney stones and gall stones are not the same thing.
Kidney stones are made up of chemicals that crystalize from the urine. The most common types of stones found in the kidneys are calcium, phosphate, oxylate, and struvite. Uric acid and cystine stones are quite rare but they do occur. If you have a kidney stone, it is important that it be analysed to see what type it is as that will help direct care in the future.
The gallbladder holds bile, which is used to help digest food. If the bile within the gallbladder is too concentrated with chemicals, the chemicals which make up the bile will crystalize out and form gall stones. As such, gallstones are made up of bile salts, cholesterol, and bilirubin.
There are no medications per say to eliminate kidney stones, though your doctor may give you medications to lower levels of calcium and uric acid in your blood. If you have a struvite stone, your doctor may give you special medication for that. Dietary changes can also potentially reduce the chances of getting a kidney stone.
There are medicines that work to dissolve gallstones, and they are called Actigall and Chenix.
Here is a helpful link about kidney stones: http://kidney.niddk.nih.gov/kudiseases/pubs/stonesadults/index.htm
Here is a helpful link about gallstones: http://digestive.niddk.nih.gov/ddiseases/pubs/gallstones/
I hope I was able to clarify for you...