Marriage license表示“结婚许可证”：

〈美〉由公共权力机关向预备结婚的人颁发的许可证，通常用以通知被授权主持婚礼的人；在大多数州的立法中，这是构成合法婚礼的重要先决条件。

A marriage license is a document you need to secure before getting married. This document does not mean you are already married the moment you finish completing it. It is like an application to get married. A marriage license can be obtained from your county clerk or from a specialized notary public. Take note that not all notaries public can provide you with this document. The latter is the better way to secure the license because you are spared the long lines typical in local government offices. The marriage license will be filled out and signed by you (the soon-to-be husband and wife) and the notary public (for authentication). The document will be completed by the officiating minister of your wedding. The completed marriage license will then be submitted by the officiating minister to the county for it to be validated, verified, and processed into the public records.

结婚许可证类似结婚申请，并非填写完毕即表示已经结婚，需要在结婚前从县书记官或专门的公证员处获得，但并非所有公证员都能提供该等文件。结婚许可证由预备结婚双方和公证员填写并签字，主婚人也需要填写，然后由主婚人将填妥的结婚许可证提交给县以便核实，随后载入官网记录。

Marriage certificate表示“结婚证书”：

由主持婚礼者签发并交由公共机构登记备案，作为婚姻关系的证明的一种文件，婚姻双方毋须签字。

The marriage certificate is an official declaration on paper that you are indeed married. It’s pre-requisite document is the marriage license. When the officiating minister submits the signed marriage license to the county, there is a considerable waiting time for the marriage certificate to be ready for receipt (in some instances this can stretch up to eight weeks). You have to remember, though, that a marriage certificate is provided only upon request. The certificate represents the legality of your marriage, the one proof that you belong to a social entity that calls for your commitment and faithfulness. It is important to have two copies of your marriage certificate as this is an important document. Marriage certificates are often required in various financial and social transactions. So keeping an extra copy is necessary.

结婚证书是官方以纸质形式宣告结婚的文件，代表婚姻合法，而结婚许可证是获得结婚证书的先决条件。主婚人将填妥的结婚许可证提交给县之后，需要等待一段时间才能获得结婚证书。需注意，只有提交请求之后才能获得结婚证书。

在我国，结婚注册登记的具体程序为：首先，申请结婚的当事人持相关证明共同到男女一方户籍所在地的婚姻登记机关用黑墨水钢笔填写填写《结婚登记申请表》；其次，婚姻登记机关接到申请后，逐项审查当事人是否符合结婚条件；最后，经过审查后，符合民法典规定的，准予登记。可见，我国的结婚注册登记的程序与西方国家不同，那么我国的“结婚证/结婚登记证书”应该如何翻译呢？可以参考下面的例句：

Couples in Jiangsu province can apply for a digital copy of their marriage certificate on Alipay using a mini program launched by the Jiangsu provincial government.

江苏省夫妻可通过江苏省政府在支付宝上发布的小程序，申领其结婚证的电子副本。

可见，我国的“结婚证/结婚登记证书”也可以用“marriage certificate”表示，因为“certificate”指的就是由政府官员或具有官方地位者对其所知的或其权限范围内的事实所作的书面的证明或确认。

参考：

Difference Between.net；

元照英美法词典；

中国日报网