Not as much as an animal, but we are learning that plants are far more sophisticated than we've traditionally given them credit for, and do have ways to detect damage (which we call "pain" in animals) and can even alert other plants to danger (which could be called "fear")

The common retort to this argument (“plants feel pain too”) is to imagine that you call the fire department because your home is burning down, and unfortunately your pet is still in the house. When the fire fighters arrive, you tell them hurriedly that your pet is inside and it needs to be saved. Without hesitation the firefighter plunged into the flames and emerges minutes later, but not holding your pet, but instead your aloe plant.

You exclaim in a panic, Why didn’t you save my pet!? To which the fire fighter says, Well plants feel pain too you know! And we’re learning a lot more about how advanced they are and how they communicate.

Do you really think you’d stand and their and consider, Hm that’s a good point, there is no relevant difference between my pet being saved and my plant?

No one who has ever made the argument that plants and animals deserves equal moral consideration due to this capacity to suffer has ever, ever meant it.

Whether or not the plant "feels pain" (and therefor whether or not it is morally wrong to do nothing while it dies in a fire) is immaterial here. People are more likely to build and maintain emotional attachments to their pets rather than their plants because their pets exhibit behaviors that are easier to identify and personify.

People want the fire fighters to prioritize saving whatever has the most value to them personally. That may happen to be house plants. Or perhaps photo albums. Or (likely most common) pets.

Okay then, let’s consider an alternate scenario then.

Let’s say that you’re a bystander at the fire, and you watch the firefighter rush into the flames. You walk up to your neighbor, whose house it is engulfed, and you ask, What are they going in for? Your puppy? to which your neighbor responds, Actually I have a really sentimental baseball glove that my dad gave me when I was a little kid. I couldn’t imagine losing the glove, but the puppy I could take or leave.

Would you understand the position, and agree that it’s better to safe the glove because it has more value to the neighbor? Or would you be appalled that your neighbor is opting to let a sentient animal burn to death in order to save a baseball glove? Albeit, a very sentimental one.

The better angle to take here would be to point out that taking an apple from an apple tree does not harm the tree. From the plant's point of view this is actually beneficial. It wants animals to take away its seeds. So this is more alike to taking milk from a cow.

Taking milk from a cow is in no way like picking an apple. Apples are intended to be eaten by any species that wants to, as a kind of quid pro quo for spreading the seeds. Cow milk is for baby cows only. Humans keep cows lactating by forcibly impregnating them, and then taking the resulting calf away. Much suffering is involved, physical and emotional.