In Canada, generally, you can only be fired (“terminated for cause”) for cause - i.e. theft, insubordination, job abandonment etc. They can terminate you without cause for other reasons, but the requirements to pay separation pay are much more strict that in the USA. It can be up to a month for every year service for more specialized jobs where it is harder to find an equivalent job. Even for ordinary jobs, two weeks or more (or a week for each year) is not uncommon. I also don’t understand the “lose pension” bit - your pension entitlement is money you earn each year that you work. they can no more take it away here, than they can steal your retirement savings bank account.
If you resign, or are fired for cause, you are ineligible for unemployment. The employer indicates the reason for termination - quit, fired for cause, or layoff - on the form.
I suspect the “resigned, not fired” is exactly - that; the person has come to an arrangement where they can claim they amicably parted ways with previous employer. A termination for cause can look really bad on a resume - better to GTFO with a nice reputation. If the person resists resigning, and the company must fire them - it is a tricky thing. Unless they can unequivocally prove a cause, they could wind up in court, and a court will decide whether the firing was for cause; if it is not, the company could be on the hook for some serious damage to the person’s reputation. The term “Wallace Damages” in Canadian employment law refers to the classic case where someone was marched out of the office and treated like crap for no good reason, and subsequently was awarded 24 months salary. And there’s no such thing as “he was a really poor performer”; either there’s legitimate cause to fire they guy, or it’s a layoff with termination pay. Trying to insist it’s “partly his fault” could bring out even harsher penalties. The courts generally find the employer, with an imbalance of power, has a duty to be fair with employees.
There’s also “constructive dismissal”. Essentially demoting an employee, whether by title or responsibilities or salary, means that they are effectively fired from their current job and rehired at the new one - so if they choose not to accept the lesser assignment, they can sue as if they were let go, and the employer could be on the hook for whatever the court deems to be appropriate separation pay.
You could fire someone for poor performance or other problems like frequent lateness; but to do so, you need to document repeated disciplinary measures and opportunities presented to the employee to try to correct their behaviour. You can’t tally up their latenesses and suddenly one day spring it on them out of the blue and fire them.
Essentially, I’m often amazed at how poorly the USA values workers and their rights compared to the civilized world.
Generally if it’s not clear whether the employer has a case for cause, or if they just want to get rid of the guy, they make an offer. “You’re heading out the door, here’s what we offer”. They may even negotiate. As one HR guy said to me, the HR lawyer’s job is to figure out an amount that’s not too much, but high enough it’s not worth the hassle of going to court for more. (I knew one fellow who was “let go” and offered 2 months’ pay after they treated him like shit; they thought as a recent East Indian immigrant he’d not know his rights. I pointed him to a lawyer who was a big-wig for the local NDP party, and they quickly settled on 6 months.)
Most places I worked had a specific policy - only confirm, “yes they worked here”, how long, and job title. Salary? Sorry, they don’t even want current employees discussing that. It’s nobody else’s business. If you say something that the ex-employee disputes that causes him not to get the job, he can sue. If you say he’s Ok and he turns out to be a dud, the employer you misled can sue you. Best to stay out of it. Rehire? I’ve seen lots of crappy employees eligible for rehire, and plenty marked “no” for petty reasons. (“He quit when I was shorthanded, it was hard to find a replacement”. Sorry, that’s your problem, not his.) Some employers simply refuse to rehire people who quit.