They can look different, but you don't specifically want the cold ones to be obvious to the dog. You want them to learn to use their nose and not their eyes!
If you start with completely random cardboard boxes you have at your house and it goes well, then you can buy an identical set of baskets or tupperware to make sure they are not using the shape of the box as a trigger.
The labeling is just to make sure you don't get them mixed up and 'contaminate' the cold boxes.
Oh and if you happen to have a dog who is shy about even going for the boxes at first, you can do a remedial introduction to a 'find it' cue by tossing/scattering a few treats out on the floor with them watching. Just say the cue immediately after tossing them and before the dog actually goes for them.
Then when you try boxes again you'll have a cue that they know means 'oh there is food for me here somewhere'