Where I live, Oklahoma, after the church funeral service, everyone eventually ends up in the "fellowship hall", which is a large room with a kitchen and a lot of tables. If the deceased attended the church, a church committee would bring in food to feed the family and all who went to the service. Family relatives would also bring food. (This is where the most interesting dishes came from, usually family favorites.)

Usually, but not always, only the family would go to the graveside for a short service and prayer.