When I first arrived in the UK in 2000, I was told about having a Dom-Nondom resident status.
I have a friend who is moving to the UK for work.
Does the UK still do this?
There are indeed some rules regarding tax for non-domiciled residents - they primarily affect income from overseas.
For example, your friend comes to work in the UK, but he owns a house in his home country from which he earns some rental income. Whether he needs to pay tax in the UK on that income depends on how much it is, whether he brings that money to the UK (e.g. by bank transfer), and so on.