As I understand it, these are two different methods of measuring stuff contained in other stuff. To answer your question, no, they are not the same. I do not know if there is a practical way to convert one to the other. There may be circumstances in which each method can be used to show the same (or similar) effective results. Be this as it may, they are not the same. *EDIT: here is some info to the contrary, from a documentary posted here many months ago. Taking it at face value, there is a direct correlation:  

Just to give a bit of history on this (recalled from aforementioned documentary), in the states, in 1941, the Department of Health (USPHS) arbitrarily chose a PPM number in the process of decreeing what the safe PPM of Fluoride was according to them. They established 1PPM as a safe value. It is important to realize that their definition of "safe value" is meaningless in the normal and accepted use of the term. It is also important to know the motive for how the USPHS came to arbitrarily decree 1PPM. Prior, there was a study done by the American Water Association (1939). They discovered that the toxicity of fluoride was on a par with lead and arsenic. As such, a PPM standard for drinking water needed to be quite low in order to remain within the genuine guidelines of "safe value" and 0.1 PPM was their recommendation. So, the USPHS's subsequent arbitrary ruling (IE> ruling of authority based on personal preference) in this instance needed to be arbitrary enough so that the industries that were backing the USPHS's position would be able to pollute, with impunity, water (and air) with their stores of toxic fluoride waste and still allow the average drinking water supply to test out at 1PPM or less. The main industry involved was Aluminum (ALCOA), which, "coincidentally" was a commercial industrial operation financed by the same person (Andrew Mellon) who had been the U.S. Secretary of Treasury during the time when the ground work for these kinds of decisions had been laid .... AND an extra hat worn by the USSoT in that day was ......... head of the USPHS.