There are multiple variations of the cufflink, the most popular being the hinged cufflink. There are plenty of other architectural alternatives to think of. Here are the ones you are most likely to find in your search.
Stud Cufflinks are not hinged. Rather, they have a straight post, larger head, and a smaller interior head. The smaller head is angled to fit into the buttonhole and then made straight to secure it in place.
Once in place, they will not move out of place, which makes them more durable.
Whale Back Cufflinks have a straight post, a flat head, and a tail shaped like a “whale” that will flip completely flat against the post. Simplicity is what distinguishes this type. Their closing mechanism, coupled with the larger post makes them easy to use. It’s the most typical cufflink around.
Chain Link Cufflinks typically have two identical heads connected by a short chain. The chain makes this style looser than others but has visible decoration on both sides of the closed buttonholes.
Ball Return Cufflinks have a small, heavy ball opposite the garnished head with a curved post. They feel looser than hinged cufflinks but a little tighter than the chain. Usually, these are created with precious metals due to the size and weight of the balls. These are a little pricier than typical cufflinks.
They come in fixed styles and are more appealing than normal bullet fixed, plain backing. They are simple to put on and provide extra looseness for the cuffs.
Bullet Back, and Toggle Closure Cufflinks are pretty close in style to whale tail shaped, but the post is hollow, and the closing mechanism is a narrow metal cylinder which rests within the frame. To secure the links in place, the cylinder is flipped outwardly 90 degrees which leave the frame to replace the post.