Which are just specific types of criminals. I don't see the problem.

Criminals are just specific types of people, and people are just specific types of mammals. Being more specific sometimes aids understanding.

I think I get what you're saying here; it's an example of the non-central fallacy[1]. Calling someone "a criminal" calls to mind a set of stereotypes, to which blackmail/extortion don't quite fit (most crimes for which one gets called "a criminal" as a generic term are violent, for just one thing.) Calling them "a blackmailer" or "an extortionist" calls to mind a more accurate set of stereotypes, clustered more closely with how you'd react to kidnappers, con-artists, etc. than how you'd react to, say, a mugger.

[1] http://lesswrong.com/lw/e95/the_noncentral_fallacy_the_worst...

Not all blackmail is a crime.

I blackmail my kids all the time... ("Wash your hands after using the bathroom or you will put 25 cents in this jar")

That's not blackmail ... "wash you hands or I'll tell your sister that you killed her pet fish" ... is blackmail. What your describing is more like extortion.