You do unless you did something illegal or ethically wrong. Not meeting some company goal or expectation isn't enough. Killing a system with a rookie command isn't enough. Being an asshole isn't enough.
Absolutely not true. Cloudflare did this because they didnt want to pay severance or even unemployment to Brittany.
In some circumstances there absolutely is a difference in the amount of money you will be entitled to in the case of being fired vs. being made redundant. It can be on the order of several months of pay. You will also see employers simply make the working conditions incredibly miserable for their employees on the hope that they'll quit instead of the business needing to make them redundant.