It's not unusual to simply not learn names for these things in Tai Chi and other chinese martial arts.
Fast forward to 20:00 or so in this video for a 30 second preview of how Chen taiji students learn to close the gap in Chen village:
... from push hands to "bridging" to standing grappling. If one studies with someone who tells him that this sort of hard play isn't required, he should go somewhere else.
He would probably dominate most people of his own weight in straight stand up grappling......its what he trains for. But put in the ability to use the ground, or a Gi and he would be a lost child.
Put him up against a good Judoka and I bet both would walk away thinking they won, Judo because he threw TCC and TCC because Judo put his knee down.
tai chi push hands are great for this
Some very friendly takedown-only sparring between a world heavyweight push hands champion from Taiwan and Marcelo Garcia:
The taiji player trains in Zheng Manqing's style and calls himself "Push Hands Chen." He was in town doing a competitive push hands seminar that was arranged by Josh Waitzkin, who is a former world push hands champ and Marcelo's first BJJ black belt.
He calls himself "Push Hands Chen."
Fun play though.