The license is the one who will be signed by the one who marry you like a cleric, judge, chaplan or other persons who have authority to marry people. After that the person who marries you send the license (properly signed) to the same court that you get the marriage license. The court (or probate court) will issue a marriage certificate, that one will be signed by the judge and by the court clerk or by the person who should signed it (varies from state to state). If you already has your marriage certificate but you want a copy, then you can get a certified copy from the same court and will have a seal on it as same as the original. Some courts give already certified copies of the marriage certificate others give original and a certified copy of the marriage certificate and others give just a certified copy.
And hello? you can copy your marriage certificate. There is no need that should be a certified copy if you want a copy of your marriage certificate. If you want that the copy should treated as an original or validated as one so you don't give up your original, then you can get a certified copy.
Now every state and even every county within the State has separate procedures and sometimes there is a waiting period, sometimes not, the fees are different and the requierements can be difference. So check at the website of the county court where you get your license.
Where did you get married (state and if it was in a court)?
Anyway, the marriage certificate says "Marriage Certificate" and the license says "License" so shouldn't be any confusion.