Geayofout60 Arcobaleno is the name of the regional fare network system in the Canton of Ticino, see their website here. More details under Tickets / Single Tickets. There’s nothing special about Arcobaleno, if buying any train or bus ticket for any journey within Ticino, you’ll simply get an Arcobaleno ticket.
Like all other regional fare networks in Switzerland, the system is zone based. So when buying a ticket for a particular connection, the vending system ensures all necessary zones along the route are included, and the number of zones determines the validity period of the single journey ticket (usually 1-2h, in some cases up to 4h). With Arcobaleno, if the itinerary includes 8 or more zones, you get an “all zones” ticket valid for 4h in the entire Ticino network.
That Ticino Ticket (I never had one) apparently refers to Arcobaleno as partner, so it looks like you’d basically get an Arcobaleno all zones day pass with that. Which of course also would include the Lugano - Locarno stretch, and therefore entitles you to have your excess luggage transferred to Locarno for a fee according to the conditions stated here.