If you ‘hire’ someone, you employ them.

We hired him on a six month contract.
I hear that they are not hiring people at the moment because of budget problems.

If you ‘fire’ somebody, you dismiss them from their job, usually because of something they did.

I had to fire Sally because she kept on making mistakes.
If you don’t improve, they may decide to fire you.

If you ‘make somebody redundant’, you dismiss them from their job for economic reasons.

They are closing down the factory and making 500 people redundant.
I was made redundant from my last job.

If you ‘recruit’ people, you persuade them to work for you.

We need to recruit more young engineers.
It’s difficult to recruit people because our pay is so low.

If you ‘headhunt’ someone for a job, you approach them because you think they are well-qualified for the job and offer them the job.

We need to look at the people doing similar jobs in other companies and headhunt the best one.
He was headhunted at great expense but the job didn’t work out and he left.

If you ‘hand in (or give in) your notice’, you tell your employer that you are going to leave the company.

*She handed in her notice this morning and is leaving at the end of the month.
He gave in his notice and they told him he could leave straight away.

If a company ‘gives someone notice’, they tell them that they are going to lose their jobs.

The company only gave me three days’ notice that I was being made redundant.
We have to give her two months’ notice that we are letting her go.

If an employer ‘sacks’ someone, they fire them.

They sacked me without notice after ten years with the company.
I hear they intend to sack him because of his bullying.

If you ‘get the sack’ or are ‘given the sack’, you are fired.

He was given the sack because he kept arriving late.
If I keep making mistakes, I’m going to get the sack.

‘Severance pay’ is money paid to workers when they are made redundant.

The redundant workers were given 26 weeks’ severance pay.
After ten years, I got three days’ notice and no severance pay.

If you take legal action against your employer for ‘unfair dismissal’, you claim that they dismissed you for no good reason.

He is suing them for unfair dismissal as he says he was only ever late once.
Dismiss me and I’ll take you to court for unfair dismissal. I’ve done nothing to deserve this.

If you take legal action against your employer for ‘constructive dismissal’, you claim that you were forced to leave your job because of the actions/behavior of your employer.

She is making a claim for constructive dismissal because she claims her immediate boss bullied her.
I’m sure you have the grounds for a complaint of constructive dismissal.