(1) "Hard-Surface Trail" is a euphemism for "Paved Trail", which is a euphemism for "Urban Wasteland Unit". One of these is optimistically defined as a trail tread surfaced with some kind of hard, stabilized material. Lovely, right?
(2) A trail intended to serve multiple uses by providing stable, firm and slip-resistant surfaces, which are always the bestest. Surfacing materials include concrete, asphalt, crushed stones, or native soil with binders. True. Some call that a "trail".
These "trail" things have smooth enough surfaces for street bicycles, in-line skates, and strollers. Many of them are also classed as bicycle pathways which are intended to serve exclusively for pedestrians and bicyclists and form a right-of-way completely separate from motor vehicles. Unless you also get skateboarders, electric scooters, motor scooters, motorcycles, and so on.
(3) A thing longer than it is wide (which makes it a trail-like thing), connecting two points (the beginning and the end). Without the middle part doing the connecting, the ends tend to drift off and get into trouble, but the middle part sometimes has a life all its own as well, especially where "trail" and "multiple-use" and "paved" meet for a showdown.
A hard-surface trail is one that has a tread finished with asphalt, concrete, or anything else that won't wash away or wear down without a fight, and tends to be found in (yes) or near (still yes) cities. (If in doubt about how close you are to a city, you can look for broken glass and used needles.)
If you are interested in sharing your walking experience with street bicyclists, in-line skaters, baby-stroller-pushers, leashed and unleashed dogs, passed-out drunks, panhandlers, and lurking creeps, then a paved trail is a place where you can find excitement.
Hard-surface trails run in what are called "corridors", have pretty-well-defined design and construction requirements, and may close at night, or whenever either the drug dealing or gunfire reach unacceptable levels. But when all that subsides and you get out there you normally find something with a minimum width of 8 feet (2.4 m) having 2-foot wide (0.6 m) shoulders, and enough fit and polish to rank as a Class One Bicycle Pathway. Think about that, a Class One Bicycle Pathway, for your walking pleasure.
Paved trails may even have painted lanes. Think about that too.
And the shoulders, ah. Shoulders, as on a highway. Got it? Shoulders. Another defining characteristic. Shoulders.
(4) Similar alternate multiple-use recreational areas: Interstate Highways. Airport runways. Strip mall parking lots.
Go have fun then. See you later, maybe.
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Me? Still searching for that one soft, quiet space not already claimed by cats.