Both of my husband’s parents had Catholic funerals. They lived in the UK and went to a parish that was predominantly Irish immigrants.
Both of them had a Vigil the night before. They brought the casket into the church and had a service - I honestly don’t remember if it was a Mass or just a Liturgy of the Word.
Then the following day was the funeral Mass. It was very similar to a regular Mass with the readings and such, but there were a few extra rituals included that I honestly don’t remember the details of.
Then after the funeral Mass, most of the people processed to the gravesite. The priest travelled with us, and did a final ceremony at the grave site. He sprinkled Holy Water onto the casket, and allowed the family members to do the same, prior to lowering it into the ground.
My grandma had a Catholic funeral too, but it was not a Mass, and I don’t remember the priest coming to the grave site.