Daylilies have a mound of leaves at the base and the bloom stalks (called scapes) are leafless and smooth, branching out into flowers at the top. Thye grow from a wide-spreading fleshy root system. You will generally get lots of flowers opening sequentially, each flower lasting a single day. There are lots of reblooming daylilies.

Lilies (genus Lilium) grow from bulbs and the stems have lots of small leaves all the way up the stem to just below the flowers. Each flower lasts several days or longer. I don't know of any reblooming lilies - you get one set of flowers each year.

- Steve

True Lilies do not repeat, they bloom once a year. Some varieties have high bud count, so they can bloom for a longer period.
You can read about Lily Culture here
and about Lily types (Asiatic is one of them) here

Thank you so much, that does clear up a lot of confusion. But adds to my lists of wants. L.O.L I do appreciiate your help,Steve and alina, I had picked up liliums by mistake the other day. I did not notice until I got home now I will be looking for more. Thanks again,Gail