Laymen, especially techies, often assume that termination for "poor performance" or "bad fit" is a "for cause" termination because there is a "cause" behind the termination, but that is an incorrect understanding of employment law.
Businesses always have a "cause" for letting someone go (usually financial or performative), so the inartfully term "for cause" actually means a cause for something other than business considerations. Generally, today "for cause" means misconduct. Each state enumerates a different set of activities constituting misconduct, but there is always some sort of misconduct involved.
(Unfortunately I no longer have the employment law book where they cover the history behind the origination of this term and I don't have the time to google an alternative history, but in a nutshell it's shorthand for a somewhat longer phrase.)
Not always. “With Cause” is defined in employment contracts quite a bit more broadly than just misconduct in all its forms. For example, my most recent contract had terms about the company hypothetically requiring relocation and I refusing as being “With Cause,” as well as things like not complying with internal rules, procedures, or org charts. Basically any reason for letting me go due to a choice I made. “Misconduct” on the other hand requires material detriment, aka me screwing over the company financially.
“With Cause” is about you being qualified for severance pay. “Misconduct” is about you causing trouble through intent or severe negligence.
That might be different for the legal term "With Cause" though. It is common for legal documents to define terms, many laws in fact start with a definition section that apply just to that law. Thus legally your state may have several different definitions for "with cause" that apply to different parts of the law.
That's cool but that's not legally for cause in the US whatever the company wants to claim. I'd go even further and say they may be violating labor law but including such a provision.
If you are terminated with case (i.e., fired), you are generally not eligible for unemployment, though there are a few exceptions.