subwoofer, a speaker, consisiting of a large woofer or more, thatd designed to play low frequencies.
bass bin, a subnwoofer, consisiting of large woofer or more, that is enclosed in a horn cabinet, to output higher SPL, and improve its efficiency, hence the horn which helps to outputs much lower frequncy. (useful, for very large outdoor venues.)
the whole use of xover is to split the audio spectrum, so that speakers play the frequencys they can handle, or the ones that they were designed for.
i.e u have a 2 speakers with a bass bin. u then xover at a certain freqnecy so that the the higher freqeuncies are played by the speakers, while the lower end is played by the sub.