Update 2016-07-03: Added updated more Wikipedia links, more words and phrases, more examples, more vocab links, more podcasts.
There are a lot of phrases in English to talk about the end of a person's employment. But these phrases can have important differences in meaning.
Here are some vocabulary lists from online dictionaries for ESL students. Click on each word in the list to see more information.
Below I'll explain some of the words and phrases, give examples and include links with more examples or info.
Quit / Quit your job / Resign / Resignation
This is the employee's decision and choice.
More info on resigning:
The noun "notice" can mean "a warning that something will happen". It is often used to mean officially telling someone that the employment relationship will end within 2 to 4 weeks.
If the employee gives notice, or gives their employer notice, or hands in their notice etc, then it is the employee's decision to leave.
If the employer gives the employee notice, then it is the employer's decision.
More info on giving notice:
Lose your Job
This is the company's decision.
This is the company's decision. It is often used to make the loss of employment sound less bad.
And there are different phrases related to the reason the employer chooses to get rid of the employee.
Fire / Sack / Get the Sack / Dismiss / Terminate
The company gets rid of an employee (usually, but not 100%) because the employee did something bad or wrong. The word "for" introduces the reason.
More information on firing:
Lay off (verb) / Layoff (noun) / Make Redundant / Redundancy / Downsize
The employee loses their job because the company wants to reduce the number of employees, maybe to become more efficient or perhaps because business is bad or the economy is weak.
(In the past, a "layoff/lay-off" was temporary, with the goal of re-employing the employee when the business situation got better. But nowadays the meaning is usually the permanent end of the job.)
More info on layoffs:
Here are some podcasts for ESL learners about layoffs, firing people etc.
A couple of interesting articles about this topic.
G.A.L.E.S.L. / joe3
Some tips and links on learning English.