How does predation on plants differ from predation. On animals in terms of the usual effect on the prey?

If a plant gets eaten by an herbivore, the plant may grow back as long as there are still buds present on the stem (or a bulb/stolon/rhizome). This is why grass doesn't die when it's cut by a lawnmower - the point where the new growth is formed is closer to the ground than the mower blades are set.

If an animal is eaten by a carnivore, it's usually eaten entirely, so it doesn't continue to live. If only a portion of the animal is affected (the predator grabs onto a tail, ear, or limb which is torn off, but the animal gets away), the animal may survive, but if injured, the injuries may still lead to the animal's death. In animals, the missing part generally doesn't grow back. But there are some amphibians and lizards which are capable of regenerating their tails and limbs, so the loss of these parts for some animals is only a temporary impairment.