Asiatics are a single catagory of Lilium, of which there are nine or ten. They are generally shorter, the earliest to bloom, produce an abundance outward pointing and upward pointing flowers. They are the most colorfull and probably the most hardy of all the different types of lilium and usually produce lots of baby bulbs pretty fast. Other common types grown by home gardeners that you'll encounter in todays marketplace are Orientals and Trumpets. Then there are hybrid mixes of all of these three--you'll see those,too.
Most shorter, border type Asiatics are candalebra type so that when you walk past them, you're looking doward and you get the best view of the flower from that angle. There are Trumpet types also, but they are much taller and used primarily as a background or center accent/focal point in the garden.
Have fun looking. And, yes, Pittsburgh really is a beautiful 'green city within a forest' Beautifull.