I too have heard them called both Spider lily and daffodil. I have some growing in two areas of my yard, but unfortunately other than knowing they are Hymenocallis, I have no idea if they are species or hybrid. I would imagine at this point they are hybrids...three different sources all planted together and in "conjugal harmony" for the last 14 years.
One group is in full sun all day., the other gets sun from sunrise til just past mid-day. Both groups are 36 inches tall, 3 to 4 inch wide leaves and they bloom in June for an extended period and then again though really sporadically at the end of summer. These images are from last year.
