a staff: the stick a person leans their weight on to walk, stand, or be steadied
At its root this word names a simple object: the cane or walking-stick a person leans on. It is built from a verb meaning to lean on or rely on something, and the form names the tool you do that with. So almost everywhere it appears, it is a real piece of wood in someone's hand.
Because the staff is the thing a body trusts its weight to, it easily stretches from the literal stick to what it stands for. A leader's staff becomes a mark of his authority. And when prophets ask what a nation is really leaning on, the staff becomes the test image for trust itself: lean on the wrong thing and it gives way, or even wounds you. These are not different words but one image followed where the writers take it.
The more abstract idea of support in general (a steadying prop, a supply that holds life up) sits at the far edge of the same picture. English Bibles reach for several words here ("staff," "stay," "support"), but the concrete cane is always close underneath.