When referring to a family as in The Duggers is it just an s or 's If the name end in a s or a z what do you do?

John Dugger and Mary Dugger have a family. They are called the Duggers. The s here is a plural. Apostrophes are never added to make a Word a plural.

John Jones and Mary Jones have a family. They are called the Joneses. The es is also a plural marker. No apostophe.

Mr. and Mrs. Dugger have a house. It is the Duggers' house. The s is already there to make the plural and the additional apostrophe marks the possessive. Mr. Dugger plays Golf. Mr. Dugger's golf clubs are in the closet. Here we add 's to the singular to make a possessive.

Mr. and Mrs. Jones live in the Joneses' house. Mrs. Jones's things are in the house and so are Mr. Jones's things. The Joneses' children's things are also in the house. Their names are James and Liz. James's things are in the house. So are Liz's

The rules:

Plural: add s or if the Word already ends in s, add es

Possessive: add 's unless it ends in s because it is a plural, then add an apostrophe.