Partial ordering vs directed ordering

Question

Let X be any nonempty set and fix a point x ∈ X. We consider the collection of all neighborhoods of x:

Nx := {A | A ⊆ X, x ∈ A}

We define a relation Nx : A ≤ B if and only if A ⊇ B.

Prove that this relation in an ordering that is directed.

I am confused with "directed ordering". Is that the same thing but differently named with "partial ordering"?

Answer 1

A relation R is directed up when for all a,b exists x with aRx, bRx.
A relation R is directed down when for all a,b exists x with xRa, xRb.
A directed order is a directed relation that is also an order.
The given (partial) order is directed both up and down.
By the context, it seems directed up is intended which is often the case.