To answer your first question:
It's a one piece mirror of highly polished metal if it is adventuring equipment.
To answer your second question:
Because it was cheaper than a silver mirror, originally
One of the things the D&D 5e tried to do during development was "unify the editions" somewhat. If you reach back to Original Dungeons and Dragons in 1974, on the Men and Magic book's equipment list (page 14) we find:
Steel Mirror / 5 gp
Silver Mirror, small / 15 GP
In play, the steel mirror was more durable and less likely to break if you fell into a pit trap (a common enough occurrence). Depending upon whom your DM was, it may or may not have been "as good" as a silver mirror in reflecting things as you used one to look around corners (one needed to be wary of medusas, yes? Dungeons are a dangerous place!)
And it was more durable
The AD&D 1e DMG (p. 80) had this note for mirrors (Table: Saving Throws for Magical and Non Magical Items):
****Silvered glass. Treat silver mirror as "Metal, soft," steel as "Metal, hard."*
The "Metal, hard" item's save versus normal blow was a 2, but a mirror's was a 15.
The "Metal, hard" item's save versus a fall was a 2, but the mirror's was a 13
... and so on for a dozen other saves.
One of the biggest benefits of the steel mirror when originally outfitting your dungeon delving character was that it cost less, which allowed you to perhaps buy better armor for your character, a better bow, or maybe buy a few more flasks of oil. Everyone rolled the same 3d6 x 10 for starting gold. Having to pick your starting equipment was a case of shopping on a budget.
Each player notes his appropriate scores, obtains a similar roll of three dice to determine the number of Gold Pieces (Dice score x 10) he starts with, and then opts for a role. (Men and Magic, p. 10)
In mosts games that I played in that era, the two kinds of mirrors were functionally identical. The amount of verisimilitude engaged in at a given table will inform how a DM chooses to differentiate them functionally, if at all, in D&D 5e. So you could call this "tradition" and be close to correct.
Mechanically, D&D 5e doesn't demand a saving throw for every item in your pack if you fall into a pit trap - some of the older editions did. A DM could, if you are walking around with a mirror in your hand when you fall into a trap, call for some kind of check or save to see if you dropped it (Dexterity check?). The DM could also rule that the fall broke it - unless it is a steel mirror.
That - durability - is a likely reason that it's the default mirror in the Basic Rules Equipment Table: what is listed is (in the main) adventuring gear rather than items from a boutique catering to the rich nobility.
Why was that distinction made?
The game was allegedly set in some vague "feudal or medieval time" (thanks to Original D&D's connection to the Chainmail miniatures war game), but within Swords and Sorcery (and Fantasy) literary genres some Renaissance era norms and tropes are not uncommon to find (see Tim Powers The Drawing of the Dark as an example). There are also plenty of anachronisms in the stories that inform D&D's general setting: JRR Tolkien's The Hobbit featured Bilbo Baggins having a clock on his mantlepiece.
Glass-fronted (silvered) mirrors existed back to Roman times, but were not common. Polished metal mirrors were much more common during the middle ages. (Thanks @Blckknght)
Note that historically decent glass mirrors appeared in Renaissance.
There is some more historical info here. (Thank you, @MarkWells)