M & E (mortality & expense) charges on VUL cash values are often only loosely related to expected mortality, more to expense. COIs are charged on (death benefit - Cash value), while M&E is charged on cash value. It really makes no sense to charge cash values for mortality, since they are already in the fund -- but tradition calls them M&E.
Current COI is often the same as mortality charge (and virtually always the same as guaranteed mortality, e.g., 2001 CSO), but some ULs include other expenses in COI as well. Most contracts permit the insurer to change current COI for non-mortality reasons, but some restrict it to changes due to mortality experience. In the 1990s, many carriers added a tax element to current COIs.