What is the difference between LTO tapes using Metal Particle (MP) and Barium Ferrite (BaFe) ?

All the older Generation LTO tapes use Metal Particle technology. This technology has limitations in how densely you can pack data on a single tape.
Starting LTO-6 almost all the manufacturers shifted to BaFe to achieve higher density. HP continued to offer both MP and BaFe Variants on LTO-6
LTO-7 onwards all the tapes are BaFe.  LTO-6 tapes are the only generation available either as BaFe or as MP from HP. Both BaFe and MP have the same specifications and will work seamlessly in the LTO-6 drive.