Neither of these wipe your record clean. But such certificates restore some of the rights that may have been lost as a result of a conviction and can help when applying for employment or a license. If you have either of these certificates, an employer or licensing agency must assume that you are "rehabilitated". This means that you should not be rejected for employment or refused a license just because of your conviction, unless your conviction has a direct bearing on your ability to perform the job.
Additionally, in New York, there are a number of laws that otherwise bar persons who have been convicted of certain crimes from working particular jobs or getting certain licenses. The certificates, in most cases, remove these called "statutory bars". Therefore, instead of automatically being disqualified for a particular job or license because of your conviction(s), you have the right to be considered for the position on an individual basis.
Obtaining either of these certificates does not guarantee a job or license. A certificate is not a pardon. It does not erase the record of your conviction. It must still be disclosed on applications if asked about prior arrest or convictions.
You can find more information at: http://dpca.state.ny.us/pdfs/certificatesofrelieffromforfeituresanddisabilitiesqanda.pdf
For more information on sealing criminal records in New York, click on the following articles:
Overview of Expunging /Clearing Your Criminal Record in New York State
Sealing of Adult Criminal Records in New York
Process to Sealing Criminal Records in New York
Sealing of Juvenile Records in New York
Do I Need An Attorney To Seal My Criminal Record in New York?