generator - has the yeast mix inside
bubble counter - has water and no yeast mix
reactor - mixes CO2 in tank water, may be internal or external, powered by water flow from pump or filter
diffuser - mixes CO2 in tank water, internal, no power, just very small bubbles and possibly a long travel path in spiral or ladder form
Start learning the lingo, it makes diagnosing things much easier!
The white snotty looking stuff is from the generator, not harmful but will make the bubbles go off track on a ladder diffuser or can plug up airstone type diffusers. A bubble counter can scrub this bit of yeast mix from the gas and keep those things cleaner, as well as allowing you to count bubbles.
If you have a Hagen CO2 system, don't bother with the bubble counter, just rinse the lid and the airline in very hot water each time you change the mix and do not shake the generator, either stir or don't stir, the yeast will mix itself anyhow.