By and large our compassion can be equal to all living beings. However, that does not include plants. According to Theravadin Buddhism, a plant has no consciousness, therefore it is not a living being, it is just simply matter. As there is no consciousness, there is no point in having compassion for it.
But as far as our compassion, we can have it towards all animals, wild or domestic, we can have it towards all humans. We wish everyone well, including all creatures, especially for those which we normally are trained to hate. Most of us are trained to hate insects as kids. Our parents did it, our big brothers and sisters, cousins and everybody else probably killed them so we also thought that's the right thing to do. Now that we are practicing Buddhist meditation we are learning a different way of viewing these creatures and understand that we don't have to do that any more, that maybe there's another way to live. So, yes, compassion can be all the same for all beings.
According to Theravadin Buddhism, animals and insects cannot be enlightened. They don't have the mental abilities humans do. So as to the basic wish that we give humans, it may be slightly different with animals. We may wish for animals to have a really good rebirth so then they can be enlightened in a different body or whatever. But that's only a theory, and we really don't have to hold onto the theory, we can still wish animals and insects well, we can wish that they can get enlightened too, because we don't really know for sure the limits of their potential.
I use this example often, the Kookaburra. A beautiful, funny, crazy bird we have here in Australia. It will adopt babies! Very interesting, it's been proven, we've seen it. Rosemary's parents used to feed the birds, they fed the Kookaburras, the Butcher birds and I think a few others on their big property. A neighbor found a baby Kookaburra that had fallen out of a tree. They couldn't get it back up there and didn't know where the parents were. So they brought the baby bird to Rosemary's parents and said, "Here, you keep it, it will be fine here."
Rosemary's parents knew nothing about this business but the neighbor assured them that since they were feeding Kookaburras this baby bird would be adopted by the Kookaburras coming to feed. So Rosemary's parents took it in, believing the neighbor, and kept it in a little box outside the back.
Whenever they fed the birds, the baby bird was there. Soon a Kookaburra came in, stared at the baby, shook his head and flew off. Fifteen minutes later it came back with a big Australian worm and immediately starts stuffing it down the baby's mouth. Incredible, this Kookaburra had probably never seen this baby bird ever before but immediately adopted the baby. And it would feed it, every day, it would come in and feed it. When the baby bird got big enough, the big Kookaburra taught the baby bird how to fly and off they went.
Now if you think about adopting an orphan off the street, most humans won't do it. Interesting? So does this parent Kookaburra have an ability that might be a little higher than in some humans in this area? We could say oh, it's instinct, well, I don't know, there are lots of other birds which actually eat other baby birds. So this is an interesting story to keep in mind about the good qualities of the Kookaburra adopting the baby.