RHF, you always provide a wealth of written and URL-referenced information
to the group, so it is with respect for your efforts that I am making some
suggestions to correct a couple of your definitions :

"RHF" wrote
"M",
.
IF you have a Single 'piece' of Wire Antenna Element
connected to a MLB (UnUn) along with a Ground Wire
and Coax Cable. Then in general most people would
call this a Long Wire Antenna; and many would more
specifically call it a Random Wire Antenna.
.
IF you have Two Equal 'pieces' of Wire Antenna Element
connected to a Balun along with a Ground Wire and Coax
Cable. Then in general most people would call this a
Dipole.
.
Dipole by Design {Tuned} :
If the Two Equal 'pieces' of Wire Antenna Element are
"Cut" to a specific length for a given frequency. Then
the Two Equal 'pieces' of Wire Antenna Element {Together}
can be said to be "Tuned" or they can be referred to as
a "Tuned Dipole Antenna".
.
Dipole by Chance/Random {Un-Tuned} :
However, if the Two Equal 'pieces' of Wire Antenna
Element are simply used to fill the available space;
and NOT "Cut" to a specific length for a given frequency.
Then the Two Equal 'pieces' of Wire Antenna Element
{Together} are simply a Random Length and can be said
to be "Un-Tuned" or they can be referred to as a
"Un-Tuned Dipole Antenna".
.
iane ~ RHF
. . . . .

You can leave out all mention of Baluns and Coax from your description of
any kind of antenna. Baluns and Coax are not part of an antenna, they are
part of the transmission line. Furthermore, neither a Balun nor Coax are
required as part of any antenna or transmission line system, they are both
options that provide either convenience or safety or both.

You may also omit the inclusion of a ground wire as being any part of a
dipole antenna. An earth ground is never part of either the antenna or
feedline system of a center-fed dipole antenna.

On the "random" or "long wire" terms, it has always been kind of laughable
to split hairs about how long a wire is before it becomes a "long wire".
Using the IEEE definition that states 2WL long for instance: for 29 mHz
reception, a random piece of wire length suddenly becomes a 2WL "long wire'
when its 66 feet long. Then, when we cut wire for 1/4 WL that generally
fulfills a good receive and transmit capability for a given frequency, it
sounds ignorant to call that a "random wire", which of course it is not.
Those two terms may always cause confusion in the field.

Best regards,

Jack