Hi brwsaw,
I tend to divide crossovers into three categories: analogue, active, and digital.
An analogue crossover, or high level crossover, resides in the speaker and divides the signal after amplification thereby only requiring one channel of amplification per speaker.
An active crossover uses analogue parts but divides the signal at line level before the amplifiers and therefore requires a designated amp channel for each section of the speaker (bass, mid, and treble for a 3-way)
A digital crossover divides the signal at line level also but does so using a Digital Signal Processor in the digital domain. This type of crossover also requires and amp channel for each section.
I guess then there is a fourth category which is an analogue/digital hybrid where the DSP is used to control the amplitude response of each amp channel in conjunction with an analogue crossover in the speaker. This is how the LFR series works.
