Cousins, removals, and how everybody is related
Two rules and the whole thing falls into place. The number tells you how far back you share an ancestor: a first COUSIN shares your grandparents, a second cousin shares your great-grandparents, a third shares the pair above those.
Removed counts the generations between the two of you. Your first cousin's CHILD is your first cousin once removed, and so is your parent's first cousin — same relationship, viewed from either end. Almost everybody who says second cousin at a wedding means first cousin once removed.
Count backwards and the numbers get silly quickly. Two PARENTS, four grandparents, eight great-grandparents — ten generations back and a child would need 1,024 ancestors, twenty generations back rather more than a million.
Go back a few centuries further and the total passes the number of people who were alive. The tree cannot be that wide, so it must fold back on itself: the same people appear in it more than once. Geneticists studying European DNA have found that everyone with European ancestry shares common ancestors within roughly the last thousand years. Everyone at a family party is related twice over, and rather more distantly than anyone would like to work out.
What other languages do with relatives
One word, AUNT, covers your mother's sister, your father's sister, and the wives of both their brothers. UNCLE is doing the same four jobs. English simply does not care which side of the family you mean.
Plenty of languages do care. Swedish has morbror for a mother's brother and farbror for a father's brother, built out of the words for mother, father and brother. Mandarin goes further, with separate terms depending on the side, the relative age and how the relationship was made. A Swedish child hears the shape of the family tree in the word itself.
MOM, MUM, mama, maman, mamma; DAD, papa, baba, tata. The same handful of sounds turns up in unrelated languages all over the world, which is not a coincidence and not evidence of a shared ancient word.
It is about what a baby's mouth can do first. Opening and closing the lips around a vowel produces ma, ba and pa long before anything harder arrives, and babies make those noises constantly while feeding and babbling. Adults hear the babble, decide it is being addressed to them, and adopt it. Parents everywhere were named by infants who were not yet talking.
Who is in the grid
The whole household and then some: MOM, MUM and DAD, the PARENTS between them, a SON, a DAUGHTER, a CHILD and a BABY, a SISTER, a BROTHER, a SIBLING, TWINS, and then out through the AUNT, UNCLE, COUSIN, NIECE and NEPHEW to GRANNY and GRANDPA.
No real FAMILY matches the list exactly, and none is supposed to. Some children have one parent, some have four, some are raised by grandparents or foster carers, and some have step-siblings whose exact label nobody has ever settled. The words are here to describe families, not to check them.