What is the difference between ψ, |ψ|², radial probability, and radial distribution of electrons?
All the four terms are different and they represent different concepts in quantum mechanics.Firstly, the term $\Psi$ represents wave function of a particle which is distributed in a three dimensional space. This wave function is a function of four coordinates ($x$, $y$, $z$, and $t$), and it gives the values which are in complex-space. For a typical example, $$\Psi(x,y,z,t) = \sqrt{\frac{8}{abc}} \sin\left(\frac{n_x\pi x}{a}\right) \sin\left(\frac{n_y\pi y}{b}\right) \sin\left(\frac{n_z\pi z}{c}\right) e^{-2\pi iEt/h}$$ is an example of a wave-function.

But the $|\Psi|^2$ is mathematically defined as $\Psi\cdot\Psi^*$. Max Born interpreted the value of this real valued function as the probability of finding the particle in 3 dimensional space. If you consider the previous example then $$|\Psi(x,y,z,t)|^2 = \frac{8}{abc} \sin^2\left(\frac{n_x\pi x}{a}\right) \sin^2\left(\frac{n_y\pi y}{b}\right) \sin^2\left(\frac{n_z\pi z}{c}\right)$$ Here the complex part will not appear as in the previous example because $\Psi$ is multiplied with its complex conjugate.

The probability of finding the particle in a unit volume element $\mathrm dV$ is $|\Psi|^2 \mathrm dV$. In spherical polar coordinates, it is $|\Psi|^2 r^2 \, \mathrm dr \, \sin\theta \, \mathrm d\theta \, \mathrm d\phi$. When you are only concerned about the radial part, the polar angular integral and azimuthal angular integral are replaced by $4\pi$ as, $\int_{0}^{2\pi} \int_{0}^{\pi} \sin\theta \, \mathrm{d}\theta \, \mathrm{d}\phi =4\pi$. thus we are left with only the radial part which is your radial probability distribution function. $$\Pr(r) = |\Psi|^2 4 \pi r^2 \, \mathrm dr$$ The radial probability can be thought as the probability of finding the particle within an interval of length $\text{d}r$ at $r=r_0$. So, the radial distribution is a function but the radial probability as described can be calculated by integrating that function from $0$ to $r_0$.