What is the difference between radioactive equilibrium and transient equilibrium?
I guess you have been caught in a semantic trap. Adjectives radioactive and transient describe  two different aspects of the same thing.
It could be as well written as &quot;radioactive transient equilibrium&quot;. Or, even better as &quot;radioactive steady state&quot;, as it is not true equilibrium.
Radioactive describes its nature . It may not be radioactive,by can be thermal, chemical, radiative, mechanical etc .
Transient describes its dynamics. It need not to be transient ( temporary, also called  a steady state ), but it can be a permanent, timeless, true  equilibrium.