Marriage: Help Civil record or Catholic Church records?

Hello Everyone,

I am trying to locate a marriage record from my Great( 3x) grandparents- Felicitas Magallanes and Cirilo (Sirilo) Alvarez married June 8, 1881 in Tlaltenango de Sanchez Roman, Zac.

As I am new to this, I have looked in the Catholic Church record with no luck. Here is the IGI listing:
https://familysearch.org/pal:/MM9.1.1/JZXY-XPK

Should I be looking in the civil records or Catholic Church records? Also it lists the date of June 8, 1881 but in the church records there are several dates listed with each matrimonial recording. Any guidance on what to look for would be greatly appreciated.

Thanks,
Pauline