It's the same in France as well, you can be fired any time the first four months, no reason needed. Equally you can also leave any time you want if you don't like the job.
So normally, you can't leave a job you don't like after 1 month? What is the process for quitting like? Here in the US, I've only ever seen '2 weeks notice' be a courtesy - you could just stop coming to work, or announce that the current day is your last.
From the perspective of professional employment, e.g. programmers:
If the employee and company part on bad terms, they can still part pretty fast. There's no mechanism to force someone to come into work (besides the threat of a bad reference) and if they did come in, there's not much stopping them spending all day distracting people and moaning about how much they hate the place.
If the employee and company are parting on good terms, the employee will hand in a written notice then work their notice period, with the possibility of ending it sooner by mutual consent. The employee generally wants to finish up what they can and hand over what they can't because they like their job and co-workers.
Needless to say, if you're a senior guy who's been at the company for years, there'll be more stuff you know and responsibilities you've assumed that you need to pass on to other people. For junior employees and recent hires, there will obviously be much less.
That's appropriate in 'right to work' states (which is most of them): you can stand up in a meeting & announce "I quit" (or hear "you're fired"), and that's sufficient notification to end your employment. In other states and countries, usually there is a notification period written into your contract which stipulates how much warning you must give the other party before terminating the contract (rule of thumb is 2 weeks + one week per year of employment).
"Right to work" is about forced union membership (i.e. "union shops"). What you are describing is "at-home employment". It's a mess of state laws and exceptions, but the only state that doesn't really operate that way is Montana.
You're right, that legal these refer to different concepts. My US employer didn't worry about distinguishing between them when I went through harassment/discrimination training.
