As you say, there are no train numbers printed on tickets. Also they are good 'till used, even if that's years from now. You buy a ticket between Raritan and New York. You ride a rush hour train and get off at Newark, with your ticket, and run to track 1 or 2 and ride a train from there to New York with that same ticket; or you can ride one of the through trains all the way with that ticket.
People don't buy a ticket from Raritan to Newark, and another from Newark to New York. That would be more expensive.
I had a guy yesterday buy a ticket from Middletown to Rahway for $7.00. Then I found out he was going to Trenton, so I took the $7.00 ticket back and sold him a ticket from Middletown to Trenton, via Rahway, for $9.00; a saving of several dollars.
You can buy a ticket from Westfield to Ridgewood, via Secaucus, one ticket. The price would probably be the same as Westfield to New York, (and the ticket would be good to New York also.) That's the way it is with Coast Line tickets, but there are exceptions that someone on here brought to my attention a few weeks ago. I don't have my ticket machine in front of me now, so I can't get actual prices. The type of train, whether it terminates at Newark and you have to take two or three more trains, with the same ticket, to get to Ridgewood, or a through train, that takes the as yet non-existent shoe-fly at Secauscus doesn't affect the price. (That will be the Raritan-Suffern local.)
Also on Transit, tickets are good on other lines where the zones and fares are the same; and if your ticket is short, you can buy a ticket for the rest of the distance.