Do you see subtle differences in the two blooms?
Neither is a true lily. Both are called by a number of common names ending in Lily. Both of the Amaryllis family with bulbs that are not attractive to rodents.
Besides the obvious differences like petal and bud shapes, here are other differences:
Crinums grow from a whorl of leaves that may or may not remain green through the winter. Here they usually die back to the ground after frost. Flowers appear on leafless stalks among the leaves mid-summer to frost.
Lycoris squamagera is frequently called 'Naked Ladies' because the bloom stalk emerges from the ground with no accompanying foliage. Another name is 'Magic Lilies' -- not magic, they have no fragrance. When bloom is over there is no further activity above ground until the following spring when lush strap-like leaves appear. These leaves wither away in early summer and the bulbs are dormant until late July when a stem suddenly appears with dark pink buds, blooming within 5 days after first noticed.
There is no rule against calling a flower that grows from a bulb and has a trumpet shape a lily. Knowing botanical names just helps distinguish one from another to other gardeners. I had trouble determining whether my Naked Ladies were really Lycoris or Belladona Amaryllis:
“The wooden spoon philisters call Amaryllis
Jersey Whites, swain and slatterns know them as
Belladonna Lilies, but only a
Mephistophelean megalomaniac such as yourself
Would dare the Naked Lady sobriquet.”
“Oh you wooly-headed arbiter elegantiarum,
You mad Corinthian, Linneaeus settled this mess
Once and for all, it is lycoris squamigera
To all but unreconstituted dilettantes.” -- Bill Sigler, Cutting
This is not a new subject, discussion of the various cultivars known as Lilies of one kind or another:
The genus Lycoris is closely related to Amaryllis, Hippeastrum and Crinum, all of which have flowers very much alike in general appearance. Hippeastrum, several species of which are cultivated tinder the name of Amaryllis, differs from Lycoris in its hollow stems and in its flattened instead of swollen black seeds. Its species all belong to the warmer parts of the American continent. The true Amaryllis belongs to South Africa, and, like Crinum, has large, round, green and fleshy seeds, and the fruit never opens by valves as in Lycoris and Hippeastrum. S. W. Garden and Forest 3: 176 (April 9, 1890)Pacific Bulb Society members discuss these and other common names at length. Sometimes I continue to think of Lycoris squamagera as Pink Spider Lilies to distinguish them from Red Spider lilies which will bloom soon.
Unlike the rose, which 'would smell as a sweet' by any other name, Lilies have varying degrees of fragrance and can be identified by scent only if there is one.
True Lily, bloomed in June.