7 June 2014 
We've all had these problems. We're at the website of a company that offers digital images of government documents. Our image-of-interest is said to come from, say, a National Archives microfilm publication. Then we're given a roll number that cannot possibly belong to that publisher or publication. (The U.S. National Archives, for example, has publications with thousands of rolls, but none have so many that the individual roll numbers carry six or seven digits.)
Being experienced researchers, we recognize those overlong numbers as Family History Library film numbers. Or we know that the online provider ran scanned images from FHL film. But we also know that we cannot couple an archives publication number with an FHL roll number and end up with a usable citation. So, how do we convert the cited FHL film number to the correct roll number for the archives who created the film?
Or maybe we have that conversion problem in reverse: We've used the archives microfilm catalog online. We know the film publication number and roll number we need to search. We want to order that on loan from FHL. How do we identify the FHL film number?
If our problem involves microfilm from the U.S. National Archives, a handy converter is available. The helpful FHL staff has provided a convenient table and a set of instructions. Use both web pages, below.
https://www.familysearch.org/learn/wiki/en/NARA_and_FHL_film_numbers
https://www.familysearch.org/learn/wiki/en/images/1/1c/NARA2FHL.pdf
Ordering microfilm for ILL or purchase
I, too, have noticed these issues; but, I have never used the option of ordering from FHL, which could be why my experience had been simplified. When ordering from NARA, a State Library or Archives, or even a local history room at the public library in our ancestor's home town, I always print the microfilm finding aid which gives me the information I'm looking for to use in a citation. While FHL has done a great job of records preservation, I'm more inclined to go to the source...probably because I've never lived close enough to a Family History Center.
Ordering microfilm for ILL or purchase
Deb, that sentence 2 is a vital suggestion.
FHL microfilm and images
The finding-aid links are very useful, but may have typographical errors.
I usually take the FHL and NARA Micropublication and roll numbers from the beginning of the roll's imaging sequence.
But there are also databases on FamilySearch that were digitally imaged directly from documents, and for which there is no originating microfilm at all -- such as the massive body of United States, Bureau of Land Management Tract Books, 1820-1908.
Source identification of digital images always requires cautious attention to details!
FHL microfilm and images
You are so right, Jade. That bottom line says it all.