I believe you are right - the two are the same. Here is how I tested it: I went to the file called genemap downloaded from the OMIM FTP site. I then looked up a handful of genes based on the gene symbol column (column 6) and extracted the corresponding MIM number (column 10). I then used these to look up the OMIM entry with this number (looking at the NO field in omim.txt.Z). In every case the OMIM entry was about the gene I started out with. It thus appears that MIM numbers and OMIM numbers are one and the same thing.
"This database was initiated in the early 1960s by Dr. Victor A. McKusick as a catalog of mendelian traits and disorders, entitled Mendelian Inheritance in Man (MIM). Twelve book editions of MIM were published between 1966 and 1998. The online version, OMIM, was created in 1985 by a collaboration between the National Library of Medicine and the William H. Welch Medical Library at Johns Hopkins. It was made generally available on the internet starting in 1987. In 1995, OMIM was developed for the World Wide Web by NCBI, the National Center for Biotechnology Information."
ID numbers have not changed for tens of years. The reviewer was merely asking you to use new OMIM acronym instead of the old MIM acronym.