Vegan, Plant Based, and Plant Strong are all terms for more or less the same thing - someone who eats plants and not animals. But it's possible to be plant based without being really vegan, or vegan without being plant strong. Confusing, I know. But I'm going to try to help you sort all this out. The simplest explanation is this: vegan is about what we don't eat, and plant strong is about what we do eat. But let's go a little deeper than that.
Let's start with Vegan, since it's what I consider myself to be, and it encompasses the other two. A vegan is someone who eats plants, plants, and only plants. No meat, no fish, no chicken, no eggs, no dairy. Vegans do not knowingly, willingly eat animals or animal products or ingredients of any kind. That's easy to grasp after a few minutes for most people, and maybe a weird question or two like, "Well, what about chicken broth? There's no meat in it." We answer those as gently as possible, and explain that chicken broth does indeed come from chickens, so no, we don't eat that. What is negotiable in a vegan diet is the quality of the food. Some vegans eat a super healthy, whole-foods diet, while others are happy with processed vegan convenience foods, which can include a lot of junk. The mere fact that a food is technically vegan doesn't mean it's healthy.
But being vegan goes deeper than just diet. Most of us are in it for the personal health benefits, at least to some extent, but we're also interested in animal rights and the environmental (and human) impact of factory farming. There are a lot of activists in these areas, and they're doing a lot of hard work to raise awareness in the mainstream population.
Vegans see their food choices as a lifestyle, taking further steps to eliminate all animal products from their lives. Leather shoes, clothing, and furniture are easily replaced with non-animal fabrics. Cosmetics and cleaning products can be found that are not made with animal ingredients, and are not tested on animals. Even things like wine and beer are often made using animal products, although a growing number of socially conscious brands are producing wonderful vegan-friendly beverages. Cause for cheer, indeed. We all add our own little twists to the theme, but basically, someone who calls themselves a vegan is doing what they do in a big picture sort of way.
Plant Based is kind of a more generic term for vegan, but it's really all about the food. A plant based eater has a very similar diet to a vegan, but may or may not choose to get into the social issues associated with veganism. As with a vegan diet, a plant based diet may or may not be healthy, although someone who goes plant based generally does it for health reasons.
The term Plant Strong has been popularized by the Engine 2 Diet, and is on the extreme end of healthy vegan diet. A plant strong diet is a whole food plants based diet that almost completely excludes processed and packaged foods of all kinds. Those doing the plant strong thing may or may not be big-picture vegans. Some are really just trying to save their own lives, and others are interested in the same social issues that vegans are.
As you can see, there's a lot of overlap going on here, and generalizing is difficult. I hope I've helped, and not muddied the waters further. When it comes to labeling yourself, don't feel like you have to. We're all doing the best we can with what we know, and the way we see ourselves will change, and continue to change, as we do. And to most of us, no matter what we call ourselves, we're all on the same team, with similar goals. We all want to make things better, and choosing plant based foods over animal based foods will always be a winning situation for all concerned. As for me, I'm a vegan, positively.