The high pressure (50 MPa - 2 GPa) - high temperature synthesized MgB2 bulk materials are characterized by nearly theoretical density (1-2% porosity), 80-98% connectivity, extremely high critical current densities (e.g. at 20 K, in range of 0-1 T jc=1.3-1.0 MA·cm-2 (doped by 10% SiC) and jc= 0.92 - 0.73 MA·cm-2 (without doping)), large irreversibility fields (Birr (18.4 K) =15 T and Birr (0 K) = 32.5 T) and high upper critical fields (Bc2 (22 K) =15 T and Bc2(0 K) ~ 42.1 T). The transformation of the grain boundary pinning into the point one in MgB2-based materials caused by increasing manufacturing temperature from 800 to 1050 °C under an increase of pressures from 0.1 to 2 GPa correlates well with an increase in critical current density in low external magnetic fields. The critical current density increase is caused by the redistribution of boron and the oxygen impurities in the material structure. As the manufacturing temperature increases, the discontinuous oxygen enriched layers transform into distinct Mg-B-O inclusions and the size and amount of inclusions of higher magnesium borides MgBX (X>4) are reduced. The effect of oxygen and boron redistribution can be enhanced by Ti or SiC additions.