One thing you'll notice on all of your patches is that they have borders around them. Some are fairly thick, too. On some, it looks really nice, but on others, these borders seem kind of wasted. They don't add much to the patch in terms of looks, so why are they there?
Patches feature die cut borders because it makes them easier to sew on to leather garments. If you try to use the heat-activated plastic backing to attach patches to leather, you're likely to ruin the material. Leather doesn't do well with heat, and it will discolor the leather and possibly do even more damage if you try to iron a patch on to it. Instead, you need to sew your patches on, which takes a little more time. However, it's worth it to keep your leather jacket or vest looking nice.
The borders are there so that you only need one color of thread. Imagine if you had a image with multiple colors that went all the way to the edge of the patch. If you used blue thread, it would look fine for the parts of the image that were blue. But when you got to the red parts, the blue thread is going to show up and look really odd. If a patch has a uniform black border all the way around it, all you need is one color thread, and you don't have to worry about it looking strange. The patch will be firmly attached and the thread will be all but invisible. That's why all types of patches, from American patches to Veteran patches, have die cut borders.