A lot of what you're saying is getting lost in the weeds of semantics I think.

Much of the wikipedia article links to this source: Pearl, Tracy Hresko (2015) "Crowd Crush: How the Law Leaves American Crowds Unprotected," Kentucky Law Journal: Vol. 104: Iss. 1, Article 4.

Which says (emphasis mine):

C. Crowd Psychology

Despite what the incidents described above may suggest to people not well-versed in crowd science, studies have consistently shown that crowd behavior is rarely irrational or "crazed."t ° Instead, scientists have found the opposite: "that an unorchestrated crowd behaves rationally."" ° Scientists assert that this rationality is present in crowds because, in most situations, "members of the crowds have dear knowledge of what and where their goals lie": entering a stadium, moving closer to the entertainment, returning to the parking lot, etc.

Furthermore, despite what media accounts of crowd incidents may suggest, there is very little evidence suggesting that crowds are prone to panic or unreasonable behavior. 12 Not only are documented cases of true crowd panic "surprisingly scarce in the literature,"1 13 closer investigation of such incidents usually reveals both (a) that the crowd responded rationally to a real or perceived threat,' and (b) that "[u]nregulated competition, which is crucial to most explanations of panic, did not occur," but rather "cooperative behavior continued throughout the course of the event."1 15 Even in situations in which crowds have reacted dramatically to a real or perceived threat, subsequent investigations have almost always shown that "flight was a reasonable group reaction under the perceived circumstances" and that "mutual cooperation and assistance" rather than "destructive behavior" was the norm among individuals within the group. 1 6

However, crowds are often unfairly deemed irrational or "out of control," because of a characteristic that is inherent in almost every crowd, particularly those of high densities: the lack of communication between the front of the crowd and the back-1 7 "People in a crowd do not have a broad view of what is happening around them," notes one crowd expert.Instead, "psychologists have likened a crowd to a series of intermeshing behavioral cells. Each cell is comprised of a small group of surrounding people, with limited communication between them." 9 As a result, when crowds reach high-risk densities, people at the back of the crowd may continue to press forward even though individuals at the front of the crowd are in severe distress 12 ° Indeed, unless the venue has some way of both overseeing and addressing the entire crowd, embers at the back of the crowd have virtually no way of knowing that a crisis is occurring up front.12' Moreover, in many situations, "[t]he collapsing of the front ranks [of the crowd] gives a false perception of forward movement" so that individuals at the back of the crowd may reasonably believe that all is well and that the crowd is continuing to move forward smoothly. 122 Thus, contrary to frequent allegations that crowd members behaved badly during crowd crushes, the overwhelming bulk of available evidence suggests that crowd members behaved rationally under the circumstances in virtually every crowd crush incident on record.

This rational behavior on the part of crowds is scientifically significant because it means that crowds are highly predictable-even in emergency situations-and that "[t]he motion of a crowd can therefore be modeled using engineering principles."12 3 This predictability is also highly significant to the legal notions of breach and causation (and thus liability overall), as discussed below.

Something that isn't really captured here is how a crowd can generate so much force. I guess the pressure is increased as each "cell" absorbs the push from behind and adds more of their own push.

I don't think the terminology really helps because the nuanced difference between different types of incidents is lost on me.

It might be better to simply say that deaths in crowds are never caused by panic, but rather the mismanagement of crowds leading to too much density.