Arbitrary? You have the same parents with sibling; with cousin you share only one of the two pairs of grandparents.

Actually that's often but not always true -

    brother b1 and sister s1 from family 1, with parents g1
    brother b2 and sister s2 from family 2, with parents g2
    s1 has child x with b2 - x has grandparents g1, g2
    s2 has child y with b1 - y has grandparents g1, g2

x and y are cousins, and also share the same 2 pairs of grandparents :-)

It can get even more fun!

If instead of two brothers marrying two sisters, you have two brothers marrying two first cousins, like so...

    b1 and b2 are brothers
    c1 and c2 are first cousins
    b1 and c1 marry and have child x
    b2 and c2 marry and have child y

... then x and y are both first and second cousins (and their children are second + third cousins, etc).

Those are "double first cousins". I even have some triple cousins in my tree, where three siblings from one family married three siblings from another family.

Agreed: in the case of siblings you share all ancestors; with cousins only some. In that way the distinction makes sense. The other way to look at it though is that with siblings your common ancestor is one generation up. With first cousins, it's two. With second, it's three. So it's the same thing, just a matter of degree.