It depends upon the state and the actual crime. In Washington State I believe it is as follows:
1st Degree Assault - A great bodily harm is caused. A serious injury that may be permanent.
2nd Degree Assault - Substantial bodily harm, e.g. broken bone that will heal.
3rd Degree Assault - Harms caused during the course of doing work, e.g. police work, injuries caused while resisting arrest.
4th Degree Assault - Offensive conduct in the mind of an ordinary person. No actual injury is required.
First and second degree assault can be punishable up to 10 years, depending upon the circumstances.