Marriage license is what the marrying couple gets to give to the officiant (priest, preacher, judge, etc.). This license states that the officiant can legally marry the couple together. Then, the designated witnesses sign the license testifying that the officiant has married the couple. And lastly, this signed document goes through the court system which will be returned as a wedding certificate.
So in other terms, a marriage license is what the couple gets before marriage; and the marriage certificate is the document obtained after the marriage. In order to receive the certificate, it is necessary to have the marriage license and some kind of wedding ceremony first. Whether it's just at city hall or in a church, a marriage has to take place to be legally married and receive a marriage certificate.
Below details in obtaining the wedding license in New York: http://www.health.state.ny.us/vital_records/married.htm
Below details in obtaining the wedding license in New Jersey: http://www.state.nj.us/health/vital/marriage_apply.shtml