Is there a semantic relationship between the Piel and the Hitpael?

I’ve seen the seven binyanim organized as three actives corresponding to three passives and then the hitpa’el as being separate.

However, I recently saw a table that listed the hitpa’el as the "reflexive of the intensive". I’m trying to figure out if that is a way of thinking that makes sense. Beyond vowelization, is there a semantic relationship between the meanings of Pi’el verbs and Hitpa’el verbs, the way there is a relationship between the meaning of Pi’el and Pu’al verbs?