I feel like it can be hard to find an exact answer to this question because I think they can be used for literally anything. To put it shortly, buttons are tiny 88 x 31 pixel sized boxes that are used to link a website/blog. Think of them as tiny advertisements! Buttons can also be used to link/advertise a cool site, art pages, fandom sites, games- literally anything you want tbh! The world is your oyster when it comes to web buttons!
Another thing to note, blinkies and stamps are not really the same as buttons. I used to get them mixed up all the time. I would say the main thing that makes blinkies, stamps, and buttons different from each other are their sizes and designs. Stamps are somewhat larger and usually have a frame around them similar to postal stamps, blinkies are long and slender and aren't usually hyperlinked to a site.
Hopefully you find this description somewhat helpful!
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So now you know a little bit about buttons, stamps, and blinkies- YAY!! Next thing I wanted to bring up were ID buttons and antipixels (yes, there's more lol). So, ID buttons (or identiy badges, userboxes, etc.) are slightly smaller than web buttons (ID buttons are usually around 86 x 15). From what I've seen, ID buttons are mainly used to display different types of identities such as gender, sexual orientation, nationality, relationship status, disabilities, and so much more. ID buttons will have rounded edges and contain an icon on the left side followed by text.
Not much can really be said about antipixels for I feel that they are somewhat similar to the ID button. Just like ID buttons, antipixels also have an icon/image on the left side followed by text on the right. I would say that the main difference between the two is that the corners of an antipixel are angled, giving it a rectangular shape similar to web buttons, blinkies, and stamps.
This is a button (88x31 px)
This is a blinkie (150x20 px)
This is a stamp (99x56 px)
This is an ID button (86x15 px)
This is an Antipixel (80x15 px)