Difference between Buried Photodiode and Pinned Photodiode
This is a commonly misunderstood misused set of terminologies.

First off these are not PIN Photodiodes - which stands for P - Intrinsic- N.  These have large depletion regions for higher internal QE (Quantum Efficiency)  and faster response.  You can't make an array with this design though.

Pinning, refers to fermi-level pinning or pinning to a certain voltage level.  Or also the forcing or prevention of the fermi-level/voltage from moving in energy space.

You can get surface state pinning from the dangling Si/SiO2 bonds providing trapping centers.  A buried PD (Photodiode) has a shallow implant that forces the charge carriers away from these surface traps.  The Si/SiO2 surface  contributes to increased leakage (dark current) and noise (particularly 1/f noise from trapping/de-trapping).  So confusingly a buried PD avoids pinning  of the fermi-level at the surface.

A pinned PD is by necessity a buried PD, but not all buried PD's are pinned.  The first Pinned PD was invented by Hagiwara at Sony and is used in ILT CCD PD's, these same PD's and the principles behind this complete transfer of charge are used in most CMOS imagers built today.

A pinned PD is designed to have the collection region deplete out when reset.  AS the PD depletes it becomes disconnected from the readout circuit and if designed properly will drain all charge out of the collection region (accomplishing complete charge transfer).  An interesting side effect is that the capacitance of the PD drops to effectively zero and therefore the KTC noise \$ q_n = sqrt(KTC) \$ also goes to zero.  When you design the depletion of the PD to deplete at a certain voltage you are pinning that PD to that voltage.  That is where the term comes from.

I've edited this Answer to acknowledge Hagiwara-san's contribution. It has long been incorrectly attributed to Teranishi and to Fossum (in CMOS image sensors)