Radiation resistance is pretty much what the writer wants it to be.
Consequently, it has to be explicitly each time it's used whenever an
ambiguity might arise. It's simply a resistance whose "dissipation"
(absorbed power) is the amount radiated. Most writers would probably
argue that power lost from the near field to nearby lossy objects such
as ground never got radiated, and therefore the corresponding resistance
should be considered loss rather than radiation resistance. The presence
of nearby ground, however, can also change the value of the remaining
resistance due to mutual coupling and alteration of the current
distribution, so a particular antenna doesn't have a single inherent
value of radiation resistance independent of environment.

As for the location where radiation resistance is defined, I believe
it's common in AM broadcasting, for example, to refer the radiation
resistance of a monopole to a current loop (maximum). If this is a
different location than the feed point, the resistance (neglecting loss)
at the base will be different from the loop radiation resistance. The
ratio of base radiation resistance to loop radiation resistance will in
fact equal the square of the ratio of loop current to base current. So
radiation resistance measured at the base can be "referred" to the loop
by scaling by this ratio. (The power "dissipated" by radiation
resistance referred to a loop or any other point has to equal the
"dissipation" of the radiation resistance seen at the base or any other
point. So Rr has to differ to keep I^2 * Rr constant as Rr is referred
to points having different values of I.) The radiation resistance can be
referred to any point on the antenna, so the writer has to specify what
point is used. But one point is as acceptable as another. It's vital,
though, when using radiation resistance, that the current at the defined
point is used for calculations. And loss resistance must also be
referred to the same point if efficiency calculations are to be made.

Some authors, for example Kraus, consistently refer the radiation
resistance to the feed point. But Kraus doesn't explicitly apply the
term "radiation resistance" to a folded dipole. There's nothing at all
wrong, however, with declaring the radiation resistance of a folded
dipole to be ~300 ohms. The power radiated is the current measured at
the feed point, squared, times that resistance. It's equally legitimate
to declare the radiation resistance of a folded dipole to be that of an
unfolded equivalent, or ~75 ohms. If you do, though, you also have to
work with the current of the unfolded dipole to make the power come out
correct.

A common mistake when dealing with folded unipoles, made by at least
several prominent people who should have known better (and marketing
people who probably do know better but find it advantageous to be
incorrect), is to refer the radiation resistance to the feed point but
the loss resistance to the unfolded equivalent. This results in an
erroneous efficiency calculation that incorrectly attributes an
improvement due to folding. As I said, you can refer the radiation
resistance to either, but if you want to calculate efficiency, you have
to refer the loss resistance to the same point and having undergone the
same transformation. And when you do, you find that folding fails to
produce the often-claimed efficiency improvement.

Roy Lewallen, W7EL