It's not the same, Edward. True, software can somewhat simulate the effect, but it actually crops the image; but more importantly, it lacks the characteristic 180-degree coverage of a fisheye lens. Below are a couple of examples. In the first, I was only about three feet behind the arch:
In this one, only a fisheye could encompass the entire crater, which is about 3/4 of a mile across. First, I tried a 17-55mm at its widest setting - not even close. Then I mounted a 12-24mm - closer, but still no cigar. Only the fisheye gave me the coverage I needed to get the shot:
You mentioned "weird fish eye like effects," which reminds me of what I used to teach my photography students when discussing optics. Believe it or not, the fisheye lens most closely resembles human vision. You can easily see this for yourself. Look straight ahead and extend your arms to the sides. Move them back until they disappear from your peripheral vision. You'll notice that it's virtually a 180-degree spread. Now comes the fun part. Take a long, straight object (like a yardstick), and while still looking straight ahead, hold it horizontally just in front of your forehead. Now, slowly move it slowly upward and downward. You'll see the characteristic curve of the fisheye view, which increases as you move it higher.
Using the Fisheye Shops image above as an example, I've printed that picture about 36 inches wide. When I (or you) place my (your) nose close to the center of the image, so that the picture fills your view, everything looks perfectly normal. If you can make the image large enough to fill your screen, and get close enough, you can see it for yourself.