What is the difference between radioactive equilibrium and transient equilibrium? Consider the following radioactive decay:
$\ce{A\rightarrow B\rightarrow C}$
In my textbook, it is written that radioactive equilibrium is when rate of formation of $\ce{B}$ is equal to rate of disappearence of $\ce{B}$.  In my textbook, it is also written that when the net formation of $\ce{B}$ is zero, we say that the system is in transient equilibrium i.e. $\frac{dB_{N}}{dt}=0$ where $B_{N}$ is the number of atoms of $\ce{B}$ at time $t$. Now, $\frac{dB_{N}}{dt}=0$ means that the rate of formation of $\ce{B}$ is equal to the rate of disappearance of
$\ce{B}$ which is exactly what radioactive equilibrium is. Then, what is the difference between radioactive equilibrium and transient equilibrium? Is there even any difference between them? Pleas explain. I am confused.
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.