Why dogs get scared when they are picked up and held but cats tolerate being picked up and held?

The dogs pant in fear.

Do you mean why 'your' animals react this way?many cats dislike being held and conversely many dogs like it. Small dogs, bred to be lap dogs, especially enjoy being held in most cases. But it really all depends on the personality of the animal.Also, panting does not necessarily mean fear. Panting can mean relaxation, being too hot, and being nervous or excited.

Are you sure they're panting out of fear? I find that cats tend to tolerate being picked up less than dogs. The dogs will get used to it. Just keep doing it, and reward them when they are not fearful. They will soon associate being picked up with a treat. In time, this food treat can be replaced by petting and by giving lots of attention.

First of all, dogs pant to regulate their temperature similar to a human sweating since dogs don't sweat. Toy size dogs crave attention from owners especially picking or carrying them. Medium or large size dogs would be hard to pick up since they become heavy. Specific cat breeds are bred to stay calm and still like a rock when the cat is picked up. Other cats that do have a personality might not like to be picked up at all. It is all about animal personality and behaviour.