That is due to the intenational conferences the "named" physical quantities and invented SI. Unfortunately, there was a split in the '50s between physicists and (mostly industrial) engineers. The engineers were most interested in magnetic flux, which powered their generators. They invented the Weber of flux and called B "magnetic flux density" in units of Weber per square meter. That name was unwieldy, even for them, so someone suggested the strange term "magnetic induction". The engineers were careful not to give B the same name as E, so as not to confuse the two. Physicists know it is no confusion, after Maxwell and Einstein, that E and B are just different components of the same tensor. Several advancedl EM texts call B the magnetic field as you and I suggest.
These books also use the same unit, gauss, for B and E, in gaussian units.