I can speak to this in California. Penal Code Section 1203.4 does allow for expungement of a misdemeanor, but in a somewhat limited way. After completing probation, a defendant can file a 1203.4 motion which allows them to then answer "No" to questions about past convictions.
There is a qualification however, in that the person must reveal the conviction to government agencies, and licensing boards, (such as the California State Bar). Also, the conviction will probably show up on any Department of Justice background checks, so while it may be helpful for some employment applications, (unless the employer does a DOJ background check, in which case it will look like the person lied on the application), it is not a true expungement.
The undesignated offense is a felony on your record until you get it changed to a misdemeanor. Your probation officer should do this at your request, or you can ask the court. Getting the misdemeanor off your record would be harder, but make sure you address the felony.