Japanese wedding system is slightly different from the system in Europe.
At first, you can have religious ceremony before applying the marriage registration to the city, town, village or ward hall. This mean that the date of the official marriage and the date of religious ceremony might be different. On the other hand, there are many couples who apply the marriage registration first and have religious ceremony later, for example a half year later. Of course, the couple can apply the registration on the same day of the ceremony but it very rare due to the time schedule. By the way, the marriage registration can be applied any time, 365 days and 24 hours a day even the office is closed for general affairs.
Having a religious ceremony is now less than before. For examples, elder couple, who has second marriage usually do not have the ceremony, especially both bride and groom are married before. Then, there are two types of religious ceremony. One is Shinto style, traditional one held at Shinto shrine. The second one is Christian style, held at either real chapel of a real church or at a nominal chapel at hotel or wedding hall. Then, if it is Christian style and the priest is a foreigner, he is usually not an officially recognized priest serving at local church but an acting priest for hired!