In the Today in History pages all relationships mentioned are the relationship of the person to the Tamaringa Smiths (i.e. the five children of John Dewhurst SMITH and Joan Margaret HAGUE).
Relationships such as father, mother, grandfather, grandmother, uncle, aunt are well known and readily understood.
Great relationships are a little more complex:
In the case of grandparents, a great-grandparent is a parent of the grandparent; a 2x-great grandparent is the next generation back, etc.
In the case of great uncles/aunts, a great uncle/aunt is a brother/sister of a grandparent; a 2x-great uncle/aunt is a brother/sister of a great grandparent (i.e. for uncles/aunts there is one more “great” in the relationship than there is for grandparents – in Australian terminology).
Cousins share common ancestry:
First cousins (the “first” is usually omitted) share grandparents (i.e. they are children of brothers/sisters)
Second cousins share great-grandparents (i.e. they are the children of first cousins); third cousins share 2x-great grandparents; and so on.
Cousin relationships are sometimes described as being removed:
Once removed indicates that the person is a cousin of our parents; twice removed indicates a cousin of our grandparents; three times removed indicates a cousin of our great grandparents; and so on.
Some relationships are described as being half relationships (e.g. half uncle; half cousin). This indicates that the relationship arises from a single common ancestor. This usually happens because and ancestor has married more than once and has had children with more than one spouse.
For example, our 2x-great grandfather George Tunnicliff DUESBURY first married Mary PRINCE in 1843 and they had five children. After Mary died in 1856, George married Harriet Ellen STEVENSON, and they had three children. Because we are descended from John William DUESBURY (the son of George and Harriet), we have only half relationships with the children of George and Mary and their descendants.
We have similar half relationships with some of the descendants of our 3x-great grandmother Elizabeth SOMERVILLE (who had three spouses), and our 3x-great grandmother Sarah REED (who also had three spouses).