Between 1908 and 1915, there are two sets of Chicago death certificates listed in the Family History Library Catalog. One group (the largest) is organized by "certificate number"--the number you find in the online index. The other group is organized by "register number"--the number you find in the Chicago Death Index, 1871-1933, a microfilm index.
So, what's the difference between the two groups? In some cases, but not necessarily all, the record found in the register number group appears to be a copy of the original death certificate. The writing is neat and in one hand.
However, I don't think all of the records in the register number group are copies. I was unable to find a death record on a certificate number film today--it seemed to be missing--and when I located the corresponding record on the register number film, the record looked to be original.