The conclusion in 1 seems to be "These findings indicate that stereotypes are not the only force at work when someone is labeled either mentally ill or a terrorist.", which is highlighted in a large font. I thought you were arguing the opposite?
And in 2, the question they examine is "whether people with negative attitudes toward Muslims perceive Muslim mass shooters as less mentally ill than non-Muslim shooters". That seems like a very biased group to ask, to say the least...
An unsuccessful (victimless) terrorist is still a terrorist (e.g. someone who blows up a building, but nobody dies, or the bomb doesn't go off), not merely a disgruntled crackpot.
On the other hand, Osama bin Laden is a terrorist, but very far from being mentally ill. His Letter to America[1] clearly outlines the intent and consequence of his actions.
Terrorists are, by definition, a threat -- but mentally ill people are victims (of mental illness, of society, etc); one is fare more likely to feel sympathy for an ill person vs. someone who is deliberately inflicting terror (as a means to an end or otherwise).
Terrorists can be affiliated to a group, but 'mentally ill' is not a group.
And that's a part of the reason why the labels get attached. 'All ____ are terrorists' is a trope where many will easily fill the blank with <group du jour>. But that won't work with 'All _____ are mentally ill'. A mentally ill person is a one-off, an accident. We don't have to solve that problem because there is no systemic problem. It just happens. The best we could do is think how we could help those people, how we could catch them before they slip.
But terrorism, that's warfare, and we respond to warfare with warfare.
That's the connotation. If you are not seeing it - well, the articles discuss this. Overall it's a part of a greater pattern of how politics shapes language, and language shapes thinking. Orwell had it down back in the 50's [2], and not much has changed since.
They are socially (and legally) in different leagues.
>are there actually any studies on this, or even examples?
Yes, there specifically are[1][2][3][4][...].
I'd suggest [1] as a start, and then Google is your friend.
[1]https://insight.kellogg.northwestern.edu/article/when-do-peo...
[2]https://psycnet.apa.org/record/2018-48477-001
[3]https://www.tandfonline.com/doi/abs/10.1080/03050629.2018.15...
[4]https://www.washingtonpost.com/posteverything/wp/2015/06/18/...