A 'tip' is a payment that is voluntarily given by a customer, normally in return for services received within a business setting, for example, in a hotel, restaurant or hairdressers.
A compulsory service charge is not a tip because it is not freely given (see below). An employee will have to pay Income Tax on any tips they get when they're working, but may not have to pay National Insurance contributions. How your tax is worked out, and whether National Insurance contributions are due, depends on the arrangements, ie who the tips are given to and who decides how they're shared out.
If the employee gets cash tips direct from the customer without involving the employer, they will have to pay tax on them - but not National Insurance contributions. The employee is responsible for telling HM Revenue & Customs (HMRC) about these tips and showing them on a Self-Assessment tax return. They'll need to keep a record of the tips they get to do this. However, most employees don't have to fill in a tax return and HMRC will estimate the tips they're likely to get and give them a tax code that will collect the tax through PAYE. It is up to the employee to get in touch with HMRC if they think the estimates wrong.
Some customers may pay their bill by cheque or credit/debit card and add a tip to the payment made to the employer. If your employer decides to pass on cheque and credit/debit card tips to the employee, they may pass them on directly or to a 'tronc' (or pool), which shares out tips amongst the staff who are tronc members. If your employer passes the tip on to the employee directly, it's their responsibility to collect tax on it through PAYE. If the employer decides how the tips should be shared out, National Insurance contributions are due and it is always the employer's responsibility to collect these through PAYE
If the employer doesn't decide or influence how the money is shared out amongst the employees, National Insurance contributions will not be due. Sometimes tips are pooled and then shared out between all the staff and the person who shares out the tips is called a 'troncmaster'. When the tips are shared out, the troncmaster has to deduct Income Tax from them through PAYE. The employer has to tell HMRC if there's a tronc and who the troncmaster is - the one responsible for collecting the Income Tax through PAYE.
A service charge is an amount added to the bill before it's given to the customer. A compulsory service charge is therefore not a tip. If your employer gives it to an employee, it's treated in the same way as their wages and they'll pay tax and National Insurance contributions on it. If it's a voluntary service charge, it's treated in the same way as a tip. How you pay tax and National Insurance contributions on it depends on whether it's cash that is paid direct to the employee by the customer and that they keep, added to a card or cheque payment, or pooled in a tronc.