Yes, they are all related, they are in the genus Toxicodendron. I have attempted to grow two species of trees in that genus, Toxicodendron vernicifluum and Toxicodendron potaninii. My largest one is getting close to my height.
From wikipedia
Lacquer Tree or Varnish Tree (Toxicodendron vernicifluum or Rhus verniciflua) grows in Asia, especially China and Japan. Growing up to 20 m tall, its sap produces an extremely durable lacquer. The leaves have 7�19 leaflets (most often 11�13). The sap contains the allergenic oil, urushiol. Urushiol gets its name from this species which in Japanese is called Urushi. Other names for this species include Japanese lacquer tree, Japanese Varnish Tree and Japanese Sumac
