I can only speak to my own experience: but the the connotation you are looking for just doesn't exist.
As long as some people are let go and others keep their jobs, people will assume there was a reason they got let go...not just because the company had to make layoffs.
Short of committing a deliberate fire-able offense, being let go as part of a layoff feels exactly the same.
I think we are defining "cause" differently.
Inam referrring to an underperformer being let go for financial reasons or someone not fitting into the culture - similar to a layoff but only impacting one person...you seem to be referring to someone who gets fired because they did something egregious.
As long as some people are let go and others keep their jobs, people will assume there was a reason they got let go...not just because the company had to make layoffs.
Short of committing a deliberate fire-able offense, being let go as part of a layoff feels exactly the same.