Difference in meaning of sentences

They do mean exactly the same thing because Aunt Sally can also be how one is referred to.

In order to show the difference change the relationship to mother.

Chris and his mother, Sally, are going to the airport.

This makes sense it tells us his mother is called Sally.

Chris and his mother Sally are going to the airport.

This does not make sense because mother Sally is not how someone would be referred to, unless they’re a nun.

Hope that helps.