DAG stands for Directed Acyclic Graph. DAG nodes are nodes like transforms and joints which exist in a hierarchy. The hierarchy is a acyclic, meaning it only goes in one direction. So a child cannot be the parent of it's parent.
DG stands for directed graph. When you are using the node editor you are seeing that directed graph. All the connections between nodes have a direction, meaning the data comes from one attribute and gets put into another attribute on another node, and that connection can't be reversed). That directionality is illustrated by the little arrow on the line that connects the two nodes. The DG is NOT acyclic. Meaning that nodes can be connected in a cycle (you can see this on a parentConstraint).

Importantly, this connection is on a node level. The individual attributes cannot form a cycle.
I hope that answers your question.