What does it mean to drain into a "laundry tub?"
Just like a Washing Machine
A washing machine drain hose can go directly into a drain, but it can also drain into a laundry tub. I am having trouble finding a free picture, so here is a link to a typical one: Laundry tub on Amazon.
The main advantage of draining into a laundry tub for a washing machine is that you can install a filter (typically made out of metal mesh and thrown away when it fills up) on the output hose to keep lint out of the main drain. But another advantage, particularly if you already have a laundry tub installed, is that you don't have to do any real plumbing work when you install the washing machine - just hook up the hot &amp; cold input and the drain output goes into the laundry tub, taking advantage of the trap that is already there.
Similarly, for a condensate drain you can simply put the output hose or pipe over the edge of the laundry tub and let it drip into the tub without worrying about any other plumbing work. My A/C condensate drain used to be set up that way, but I changed it to go into a floor drain instead because the slope was too low for the long pipe run needed around the laundry room.
Draining into a laundry tub also functions as an air gap. Because the hose is not going directly into the drain pipe, it becomes nearly impossible for water to back up from the main drain into the device (washing machine drain or A/C or water heater condensate line).
What you can't do is simply drain into a bucket, except in an emergency situation. Any bucket - whether 1 gallon or 5 gallon or any other size - will fill up and overflow if left unattended with a condensate line, it is just a matter of time.