If it was a C-802, as has been reported, then it's more like a Harpoon than the sort of Exocet that got the Sheffield and the Stark. Of course any left over jet fuel for it's turbine engine could have much the same effect. Latest model Exocet also uses turbine engine rather than solid rocket.
I have limited knowledge in this area, so I defer to your expertise concerning the differences in their propulsion systems.