What is the difference/relationship between electron current and hole current in MOSFET?
In semiconductors there are two charge carriers: electrons and holes. Holes are particles just like electrons but with a positive charge (and a different effective mass, diffusivity, and other properties). Any net current through a semiconductor is made up of some amount of electron current and some amount of hole current. Your equations show the drift current density (current due to electric field) and diffusion current density (current due to variation in concentration) for electrons and holes.
Your total electron current density can be broken down as:
\$J_n(Drift)=-qn\mu_n\nabla\phi\$
\$J_n(Diffusion)=qD_n\nabla(n)\$
Where \$-q\$ is the charge on an electron, \$n\$ is the electron concentration, \$\mu_n\$ is the electron mobility, \$\nabla\phi\$ is the electric field gradient, \$D_n\$ is the electron diffusivitiy, and \$\nabla(n)\$ is the gradient of the electron concentration. The hole current uses equivalent values.

Weird stuff happens when you have charged particles in periodic potentials (which a semiconductor crystal is) which leads to these &quot;holes&quot;. Dont worry about them not being &quot;real&quot;. They are real enough for the model.