On iOS apps can check for the availability of URL schemes ("can I open a link of type ftp:"), so they can check if apps that expose a URL scheme are installed (mostly this is apps that offer an API, such as Facebook, Twitter, etc).
But, apps have to declare which URL schemes they want to be able to check for, and this list is inspected by app review. So if you want to check for every known app in existence (which some apps like IIRC Twitter used to do before Apple limited it), you'll fail app review. I'm not sure how strict they are about shorter but weirder lists of URL schemes (like a todo app checking for bank apps)
But, apps have to declare which URL schemes they want to be able to check for, and this list is inspected by app review. So if you want to check for every known app in existence (which some apps like IIRC Twitter used to do before Apple limited it), you'll fail app review. I'm not sure how strict they are about shorter but weirder lists of URL schemes (like a todo app checking for bank apps)