Hemerocallis is the botanical genus of daylilies, so a comparison of these names must specify which species or varieties are meant. Compare labeled plants rather than treating the two words as unrelated groups.
A genus and a common name
Hemerocallis is the botanical genus commonly called daylilies. The two words do not describe separate unrelated plant groups. A useful comparison must therefore identify the species, cultivar or local common name intended on each side.
Compare reliably labeled plants
Daylilies vary in leaf proportions, flower shape, color and flowering season. No single leaf-width or orange-versus-yellow rule separates every plant covered by these broad names. Compare the label, whole clump and open flowers together.
Keep the purpose of identification clear
For a garden choice, check mature size and the expected display of the named variety. When a common name is being translated, preserve the original botanical spelling so that the same plant can be traced in other references. A photograph of one flower can help describe its appearance, but it should not be used to assign other properties or uses to an unconfirmed plant.
Related reading: Daylily Care: Dividing Clumps and Supporting New Growth.