An Adorned Cross (sometimes called a Decorated Cross) is invariably based on a simple Latin or Greek cross so that the additional feature is emphasized. The additional feature usually becomes the main focus of the object; the crucifix is an obvious example. Another example is the Irish Claddagh sign, which is considered by some to have supernatural power when mounted on a cross. And yet another, albeit silly, example is the Santa Cross.
The cross enhances the feature, which may be a religious icon, a fashion item, a tattoo, a memorial, or whatever the imagination dictates.
It's interesting that with some Adorned Crosses we glorify the feature, as for example we glorify America with the Old Glory Cross, whilst other Adorned Crosses are used not to glorify the feature, as for example with the AIDS Cross.
Some of the most elaborate and richly adorned crosses are not out of place in Roman Catholic, Orthodox and 'High' churches. Sometimes it's a challenge to find a suitable name for cross with a corpus and a halo and Golgotha steps and fleur de lis and jewels, and so on. Such cross naming is often left to the whim of souvenir gift shop suppliers, who coin terms such as Vatican Cross, Adoration Cross, etc. or the rather pointless term Deluxe Cross.