Criminal assault involves actual contact; it occurs when somebody intending to cause bodily harm to another person does, in fact, walk up to said person and beat them over the head with a lead pipe/crowbar/bare fist/beer mug/brick/etc. If you do that, your local State prosecutor's office will file assault charges against you which could ultimately result in your incarceration.
Civil assault, by contrast, does not involve actual contact but instead involves the verbal threat of physical contact; it occurs when somebody threatens bodily harm to another person under circumstances where it would be reasonable for said person to believe that bodily harm is imminent. If you do that, no criminal charges will be filed against you. However, the person who you threatened can sue you in a civil court of law for civil assault.
Against that backdrop, I present to you Exhibit A, New York Republican Congressman Michael Grimm:
Thoughts?