>There is a great Web site. Then, you use iPhone to access the Web site. The page does not look like the Web site but looks like an app. It has the iPhone regular little square for the menu which offers available choices and so on. However, this is not an app I had to install. How are they doing it?
Lots of ways you can do this. If the site is completely different they are likely using a mobile specific site that is designed separately. You can check screen width or look at the user agent to determine what's coming in and then route to a mobile page for example.
The other big option is to use responsive design (CSS) to rearrange the layout of your page. You show and hide things based on the resolution of the screen. Some frameworks like Bootstrap can also help with automatically reflowing horizontal content vertically (ie. two column layouts become to stacked rows) etc.
Lots of ways to do it.
+++ Rick ---