Vice is a transgression against oneself. If what you do hurts you, it certainly qualifies as vice.
Crime is a transgression against society. Whether or not what society defines as crime is arrived at in a capricious and arbitrary manner, one can be fairly certain that in committing crime, one runs the risk of being hurt by society.
Sin is a transgression agasint god. In that god is an undemonstrated proposition, one can only said to be hurt by sin to the extent that it can also be described as vice or crime. Deadly sin is a term specific to Catholic theology, although the concept is recognized by other christians. Specifically, the Catholic church divides sins into two categories: venial sins, minor affairs for which one might be punished, but which do not imperil one's immortal soul; and mortal (deadly) sins, which imperil one's immortal soul, meaning that one is damned for eternity unless one can secure divine forgiveness.
You are, as is everyone else, free to believe what you like about the matter.