Moonblaster, Moonblaster FM, Moonblaster Wave ?

MSX-AUDIO (Music Module) is OPL1 sound chip plus one ADPCM soundchannel.
MSX-MUSIC (FM-PAC) is OPLL sound chip, this is a low-cost variation of the OPL2 sound chip.
MoonSound is OPL4 sound chip.

Most Japanese software support MSX-MUSIC. Most european software supports MSX-AUDIO (often also MSX-MUSIC). MoonSound is partly compatible with MSX-AUDIO (FM only, no ADPCM samples).

Compared to the combination of MSX-MUSIC+MSX-AUDIO, the main difference of MoonSound is the addition of 24 Wave channels. On the other hand, software to access MSX-MUSIC and MSX-AUDIO FM channels separately does not exist, so in practice MoonSound also doubles the amount of FM channels.

Music Module does output via the MSX audio, but the volume is probably low compared to PSG/FM-PAC.

Then your MoonBlaster question. MoonBlaster 1.4 works with MSX-MUSIC+MSX-AUDIO, MoonBlaster Wave and MoonBlaster FM work with MoonSound. They are limited to Wave channels and FM channels (+small amount of Wave) respectively.
For more capable MoonSound software, try MoonSound Music Studio by TNI. http://www.tni.nl/products/ms2.html

Whadaya mean? I know at least one tracker that does

Technically Oracle and, before it, SME 3.0 do support that. However, in practice both of these programs are too obscure to be mentioned, let alone recommended, especially to someone already confused.