Generally speaking, puns can be a little more involved or "wordy" tah Dad jokes but they are closely related.
funny
Things to Consider…
For the chicken, it's involved but the pig is committed.
“If-Then-What?”
If a football game has 4 quarters, why don't we call it a dollar?
How’s That Again?
Hey! Is that a Clark Bar floating over there?
These Guys Make me Laugh…
Matter-of-fact, I believe great comics get under-appreciated because their best work makes us laugh.
Johnny on the Spot 