Martin D. Pay wrote:

When I've traveled in the US, sometimes I've paid the whole bill
and tip in cash, sometimes paid the whole bill and tip on plastic
and sometimes paid the bill on plastic and left the tip on the
table in cash. Is there a preferred way (preferred, that is, by
the waiting staff)? I sometimes wonder how much the waitress sees
of a tip that goes on the plastic and so through the
establishment's books...

The wait staff probably prefer the payment in cash at the table, since
there is no record of the amount, and they get the cash directly. They
certainly won't refuse the payment on a credit card, since they typically
take the cash out of the drawer and pocket it as part of the transaction.
In some cases, the owner will distribute the cash at the end of the day
when the till is being reconciled.

There are various ways that tips are handled in restaurants. In most
cases, the wait staff keeps the tip. In some cases, all the money is put
into a pool and then divided up evenly among the wait staff. In some
cases the tip revenue is shared with the bartenders and chefs, according
to some agreed-to ratio, with the wait staff getting the majority. There
is no set rule.

There are also some shady restaurant owners who demand a cut of the tip
revenue. Those are not common.