Any tip that is on a debit or credit card is recorded and added to a server's pay. It is not usually paid at the end of the evening, but is added in as a charge tip on the server's paycheck, and paid out on a paychaeck. Cash is recorded differently, but is also recorded on the pay stub for tax purposes. It all counts as income for the server, and results in the same payroll liability for wages, both for the individual and the business. The business is liable for SS and MED as well as SUTA and FUTA, worker comp and liability insurance. Wages are wages.
In this industry, most restaurant managers insist on servers recording cash tips, and will often check total sales for servers to be sure that they are recording at least part of the cash tips. I run payroll for about 70 small businesses and have several restaurants in my roster. I monitor the wages side to be sure that servers are making at least minimum wage, and have a tip makeup built in to my system. I also caution the owners to watch how cash is recorded because the audits are not pretty. The state Dept of Revenue is generally the entity that will schedule random audits. I have never had to sit though this kind of compliance audit, but my employer has and he has advised that our businesses encourage their servers to report cash through the payroll and not rely on them reporting on their own.