Not every Android phone can run the latest version of Android. I have a HTC Dream, the first consumer Android phone, and it still runs on Android 1.6, just like yours. No updates are coming to this device in the future, unless I root it and install a ROM onto it.
As for the difference between your friend's phone and yours, some apps are only developed for a specific version of Android and up. For instance, the app in question may be developed for Android 2.0 and up. Since yours only runs Android 1.6, the app is not displayed on the market and won't work on your phone.
Unfortunately for you, if HTC says they are not going to update the handset, then it is not going to be updated by itself.
There is one way update it however. You will have to root your phone and find an Android 2.1 ROM (there may even be an Android 2.2 version) to install onto your Tattoo. Take a look here for possible ROMs: http://forum.xda-developers.com/forumdisplay.php?f=544