Given that these questions have a certain currency and meaning in contemporary writings on the topic, it was interesting to go to the Oxford English Dictionary to see how the term is defined historically.
The dictionary gives two main meanings for the verb to criminalize. The first is
"to turn a person into a criminal, esp by making his or her activities criminal".This draws a direct analogy with the French term 'criminaliser', meaning to accuse, and most of the early usages listed relate to the accusing of particular individuals with having committed crimes. It is not until the middle of the nineteenth century, that it takes on a more modern (and perhaps sociological) sense of defining individuals or groups as criminal or deviant in some way (Thus from the Law Magazine in 1854: "Young offenders had better be reformed than criminalized.")
The second meaning is that which is more familiar from philosophical writings on the topic and is
"to turn (an activity) into a criminal offence by making it illegal."