Here is the official word from the American Hemerocallis Society on the foliage traits of daylilies:

"Foliage traits of daylilies include color, size, habit, and cold-hardiness and heat-tolerance.

COLOR
The foliage of daylilies can be blue-green to yellow-green or any shade in between.

SIZE
Daylily leaves vary considerably from slender and grass-like to husky, wide, and nearly corn-like. The leaves may arch, or may stand nearly erect. The length of daylily leaves ranges from as little as 6 inches to 36 inches or more.

HABIT
The winter behavior of the daylily foliage is called "the foliage habit." For registration purposes, the foliage habit is loosely categorized as dormant, evergreen, and semi-evergreen.

• DORMANT. The leaves of these daylilies die completely back as winter approaches. They stop growing and form resting buds at the crown, and foliage dies down naturally and gradually. In the spring, the resting buds have a distinctive spear-like appearance as they emerge.
  
• EVERGREEN. These daylilies retain their leaves throughout the year. They do not form resting buds. Instead, they continually produce new leaves unless cold weather prevents growth. In mild climates, the leaves of evergreens remain green all winter. In the coldest climates, the foliage of evergreens nearly always is frozen back, but the crown survives if it is hardy (or well mulched).
  
• SEMI-EVERGREEN. Today, the term semi-evergreen is used to describe any foliage behavior that is not readily classed as simple evergreen or dormant. Originally, the term semi-evergreen (or conversely, semi-dormant) was used to describe those daylilies that retained many of its leaves and appeared somewhat evergreen when grown in the South, but lost all its leaves and went dormant when grown in the North.
  
  

Note (1/29/19): Not only is the American Hemerocallis Society transitioning to a new name (American Daylily Society), it is also transitioning to a new term for dormant foliage (deciduous).
"This term refers to the winter behavior of daylily leaves. Daylilies are either deciduous, semi-evergreen or evergreen. This indicates how the cultivar’s foliage passes winters in the hybridizer’s garden, but is not necessarily an indication of how it will behave elsewhere under differing environmental conditions. Note that hardiness and foliage habit are inherited separately, thus not all evergreens are tender and not all deciduous plants are hardy."

COLD-HARDINESS AND HEAT-TOLERANCE
"The cold-hardiness of daylilies is quite variable. Some are ironclad hardy. Others are extremely tender. Cold-hardiness is not determined by the foliage habit. Evergreen, dormant, and semi-evergreen can be anything from extremely cold hardy to extremely tender. To avoid risk of losing a cultivar, choose daylilies that others have already grown successfully in your climate." (Brown's Ferry Gardens)

That being said, all plants registered as a given foliage type may not always be that foliage type. A cultivar may perform differently in your garden than it did in the hybridizer’s garden, due to differences in growing conditions. It's also possible that a seedling gets labeled wrong or that there is a mix up in the process of registering a cultivar.

In essence there really are only two foliage habits: dormant and evergreen. The semi-evergreen category is actually a catchall category (to which the AHS alludes above) for any cultivar that is not completely evergreen nor completely dormant. Often the degree of dormancy is in the eye of the beholder.

Finally, the generalization that all evergreens are tender and all dormants are cold hardy is not always true. There are cold hardy evergreens and tender dormants. For a list of evergreens hardy in zone 5, see my blog post, "Evergreen Daylilies Hardy in Zone 5" at https://cottageinthemeadow.plantfans.com/BlogPostsByTag/DAYLILIES