[Physics] Displacement vector vs position vector

classical-mechanicsdisplacementvectors

Below are my attempted definitions of the two terms. Are these correct and do they clearly distinguish between the two terms?

My understanding is that the displacement vector comes first and that is then used to define the position vector.

Definition 1. The displacement vector between two points $A$ and $B$ is the vector $\overrightarrow{AB}$.

Definition 2. The position vector of a point $A$ is the displacement vector between the origin $O$ and the point $A$.

Another related question: If Definition 1 above is "correct", what then, if any, is the formal distinction between a displacement vector and a vector?

Related: 1, 2.

You are correct that a displacement vector between $A$ and $B$ is generally the vector $\vec{AB}$ defining the displacement a particle would make going from point $A$ to point $B$.
The position vector is just the (displacement) vector from some arbitrary but defined reference point, usually called the origin, $O$.
The key to remember in the end however is that they are all just vectors ie: $vec{AB}$, $vec{OA}$... and that they all share the same properties and operations. There is nothing special about the position vector vs the displacement vector other than the name allowing us to quickly associate it with a given starting point.