A Be star is an early star, generally a B-type star, with emission lines such as hydrogen Balmer lines. Such an A-type star might be lumped in as a Be star or alternately, might be termed an Ae star. The same for an O-type star.
Current theory is that Be stars 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 Be star and a B(e) star are different types, the latter being a B-type star with forbidden emission lines.