How are those photos that you can see the extremity of the lens taken?

There are a lot of photos where you can see the photo and that circle of the extremity of the lens. I know it's something called fisheye, but there are some photos where you don't see it. I'm thinking about buying a Nikon D3100 and it has the fisheye mode but in some photos it's just a photo more rounded. I just searched for a fisheye lens and the result was the same.

Here's some photos of what I'm talking about (the rounded photos):

And what I'm looking for (the extremity of the lens):

Added (1). If you can't open the links just copy them and paste on the url bar xD

The fish-eye effect is produced by a fish-eye lens. Some cameras and most softwares can artifically produce a similar effect - I gather that the D3100 can produce it, from what you say.

Good fish-eye lenses are expensive. Sorry, couldn't open links.

There doesn't seem to be a question here. Fisheye lenses or software can produce a fisheye image. The lenses are expensive (as are the cameras that use them) but the result is better.

The photos where you can't see the camera lens extremity are taken with an actual fish eye lens or a wide angle lens such as a 10mm for example.

There are also lens attachments such as the lensbaby. Its usually these attachments that show the extremities of the lens.

You can also add a "fish eye" effect through photo software wether it be on the camera itself or on a computer.