Your distinction is right OP and on target...
All headphones i ever used were able to give deep loud bass...
Not one give me tactile bass... Save my modified AKG K340 ... I listen big organ bass notes in a church with my toes and body ... The first time i was so surprized it felt like an acoustic hallucination...
The reason is the way the dynamic membrane of this hybrid headphone and his 5 tuned passive resonators acting as woofer are able to go deeper without loosing any power under 40 hertz to 25 hertz, without any flowing from the deep bass in the mid bass ...
Erik_squires will be able to explain it better than me about membrane design ...