In the last 40 or so years the term has shifted to mean permanent termination.
That said, this article gives zero indication this is a firing, so I expect that your parent's comment is someone who is salty at Twilio and wants to make this sound "more vicious" -- 'firing' someone is a harsher sound than 'laying them off'. Plus, there's VERY few examples ever of significant staff cuts happened with _firings_. That would imply that 17% of Twilio did something so egregious at work that they got fired all simultaneously, which, like...how?
That's not how I'd use those words. "Fired" just means your employment was involuntarily terminated. Layoffs are a type of firing, at least to my ears.
I don't see anything in the Twilio post that looks anything like a firing.
Firing a person tends to mean that the position will be hired for again once the person is gone.
Another way of looking at it:
Firing a person is terminating an individual working with a company - but the company still has that role to be filled.
Laying a person off is the elimination of the role, which also has the person leaving the company, but its the role that is being removed, not the person (they are free to apply for other positions in the company or get rehired later).
When you are fired there is a direct implication of fault or failing to perform.
These things can vary a lot depending on local/state/country laws, but if you are laid off you may be entitled to a redundancy payment, you may be entitled to apply for other roles in the company², you will have a notice period which you will either work or go on gardening leave for, and so forth. If you are fired, none of this applies³. If you are in an work-at-will state things are a bit different. Gig economy jobs are a grey area in many places⁴.
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[1] other than the implication that the people who kept the same/similar role are better or otherwise more useful to the company
[2] if the lay-offs are due to restructuring rather than downsizing
[3] except you have access to some sort of appeals process (for unfair dismissal for instance) which goes your way
[4] there are court cases and other investigations ongoing to determine/clarify what rights such workers do[n't] and should[n't] have
There's absolutely a difference in widespread RIFs/layoffs and firing an employee, both in terms of how that individual is treated by future potential employers as well as the eyes of the law.
If, however, you're suggesting that there is in fact no difference between individual involuntary termination without cause and a mass involuntary termination without cause, then the WARN act in CA is just one such counterexample, and very clearly treats "plant closing or mass layoff" as a specific event, separate from other types of involuntary termination without cause.