As to the first, the part the customer retains is called a stub (the returned portion of a ticket ), and the other part is sometimes known as the counterfoil (though the term can be applied to other things similar to tickets such as bank wires ). “The second could be tearing or detaching (there’s not a specific term just for tickets, that I know of), while the third is a perforation.

You can even borrow the term Counterfoil from my answer and use it to make it complete — but attribution goes to user11761.

When a part is detached from its friend, the detached parts become stubs. What is meant by “when you go to the restroom, remember to bring your ticket stub with you. “? If there’s a word for the half the box office retains, or would it be a popular one, “Adopt it”?

The Oxford English Dictionary finds ticket stub in use by Ellery Queen in The Roman Hat Mystery (1929): “You’ll be looking for ticket stubs.” Everything resembling half a ticket. “The earliest definition given for stub, from the year 967, is as a synonym for “stump” (of a tree); many or most of the definitions that have evolved since then retain the sense of a small thing that has been severed from a larger thing—like a ticket stub, in modern times.

“BATH-HOUSE ROBBER: No need lookin’ fer allin’ here, Bill.

Ticket receipt for one of Joe Cook’s lectures, an’ a poker chip. Busted drummer from Montreal! I

guess you had to be there”

The customer’s part is usually called a stub. (For example, restaurants near cinemas will sometimes advertise a discount “with a ticket stub”. The act of separating the two parts is sometimes called “tearing”; alternatively, the overall act of a gatekeeper being handed your ticket, quitting, and giving you the part back is often “taking a ticket”, same as if you didn’t get a part back.

How does the venue keep a specific word?

A counterfoil is the part (the whole) of the ticket which is retained by

the issuing authority. C is the symbol of the counterfoil not stated. (See table)