Usually, I consider someone related to me if we share a common ancestor. This definition encompasses ancestors, descendants, siblings, cousins, super-siblings (my general term for uncles and aunts) and sub-siblings (my general term for nephews and nieces).
But this definition seems a little arbitrary, as it consider only the divergence of lines, while ignoring the convergence. Divergent genealogy (as I'm now calling it) says I'm your relative if we share copies of an allele that once resided in the one human being, or we can both at least trace a line of parenthood to one human being. But if you and I share a common descendant we are not necessarily related divergently. So, I now define convergent genealogical relativeness as meaning that two people share a common descendant. Convergent and divergent genealogy both recognise ancestors and descendants as relatives.
Time for some new terms (invented on the spot by me, in brackets what it looks like if the family tree is upended):
coparth: the other parent of one's child (upside-down sibling).
first retrocon: another of the grand-parents of one's child (upside-down first cousin).
second retrocon: another of the great-grandparents of one's great-grandchild.
first retrocon, once lowered: one of the grandparents of one's great-grandchild.
first retrocon, one raised: one of the great-grandparents of one's grandchild.
first-order supercoparth: a grandparent of one's child.
first-order infracoparth: a parent of one's grandchild.
The generalisations are left as an exercise.
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