A Be star is an early star, generally B-type star, with emission lines, generally hydrogen Balmer lines. An A-type star might be lumped in as a Be star or called an Ae star. Similar for O-type star.
Current theory is that they are rotating rapidly, and heating a circumstellar disk of gas ejected by the rotation. Many show overlaid H-alpha emission and absorption lines, each with considerable line broadening, the former indicating the rotation of the disk and the latter, the rotation of the star.
A B(e) star and a Be star are different types, the former being a B-type star with forbidden emission lines.