Self-forces and backreaction in electromagnetic and gravitational forces In classical electrodynamics is well-know the concept of self-force or self-interaction of any particle (much unlike two-body forces ruled by newton or coulomb forces!).
What is the relation between self-force and the so-called radiation backreaction in electromagnetic and gravitational relativistic theories?
Bonus: is self-force already quantum in the sense of nuclear forces self-interactions via Yang-Mills equations/theories or is this concept a different one? Can we define quantum radiation backreaction in Yang-Mills theories too?
 A: Self-forces and radiation (back)reaction are related through so called "balance laws". These state that the long-term average changes of "conserved" quantities such as energy and angular momentum due to a self-force are equal to the long-term average loss of energy or angular momentum through radiation to infinity (or absorbed by event horizon(s)), i.e. radiation reaction.
These laws are typically only valid because locally in time, self-forces will depend on the choice of gauge. Moreover, in the gravitational case, the flux of energy and angular momentum is only well-defined as a time average.
Radiation reaction forces can therefore considered a component of the full self-force. In particular, the radiation reaction force is the secular dissipative part of the self-force. Self-forces can and do contain conservative components leading to observable (gauge invariant) effects. For example, the gravitational self-force on an object orbiting a black hole leads to a correction to the frequency of the "innermost stable circular orbit" (ISCO) linear in the ratio of the masses of the object and the black hole.
As the to your bonus question: There is nothing quantum about self-forces, and the concept is completely separate from the self-interactions you might find in Yang-Mills theories, which themselves are nothing inherently quantum. These "self-interactions" simply express that we are dealing with a non-linear field theory, which could be either quantum (e.g. QCD) or classical (e.g. GR). Self-forces occur in both linear field theories (e.g. electrodynamics) and non-linear field theories (e.g. GR). While the language of self-forces usually implies a classical setting, similar calculations occur in quantum theories. For example, the Lamb shift in QED could be considered a quantum self-force effect.
