I went through layoffs four times in a row after working at each one for less than two years. Each time it was due to a downturn in the company due to poor executive decisions (in hindsight) or bad timing with the market. I actually started thinking I was cursed, and stopped taking as many chances because I saw too many companies struggle and fail up close and personal.
There was also a period of unemployment in between each one, and my finances took a beating each time (seemed like I had only just recovered when the rug got pulled out from under me again). It sucked. I'm still struggling in some ways as a result of it, years later.
People sometimes use them interchangeably, but it's a courtesy to say "laid off" if someone is simply gone because of a budget cut/re-org/merger/acquisition.
I've been divorced with a kid. It's been over a year and I'm still in therapy. My identity was shattered.
Like you, I have never defined myself by my job, it was what I did to provide for my ... family. Divorce hit me way harder financially as well than job loss. No job every took 50% of my assets and future assets with them.
I've been both divorced and fired. I got fired because my position was outsourced to India. I got divorced because nobody liked me :).
The firing was basically nothing. I think the key difference, for me as an individual, is that I'm not a "lifer." I'm generally well liked in my jobs and get regular raises and promotions, but I'm not emotionally attached to the vision or whatever. In addition to that I happen to be the type of person who keeps a hefty emergency savings and all that. Financially speaking getting fired was a minor nuisance. I had another job within a month.
Getting divorced was really tough. It was an existential crisis. One day I was one thing, a married man with a child. The next day I was this completely different person, a bachelor with half a child. I didn't have ANY single friends, or childless friends who could do adult things when my daughter was with my ex-wife. I had to re-create who I was almost from the ground up.
The key factor, for me, is the "lifer" status. I was a lifer in my marriage, but have never been for a job.