Is there a way to wrap any website as an iOS app?
If you are looking to make your own app using web technologies, there are some options. Look into Cordova and PhoneGap. There are similar alternatives for making apps for desktop operating systems as well.

While they may be easier to develop depending on your existing skill set, they may not feel as fluid as native apps. While some developers do a great job making HTML5-based native apps or even hybrids, often times they feel non-native to the user.

If you have an existing mobile-friendly website that you want to package into a native app, you can probably make a basic app with a UIWebView that merely displays the website. This will almost definitely feel like a website to the end user.