Virtually all modern colloidal silver generators use a variation of constant-current output to produce Colloidal Silver. Constant-current, just as it says, limits the current output of the generator and keeps it steady within a narrow range. This prevents the generator from "snowballing" and producing large particle sizes and an unusable product.
Very pure water is a poor conductor of electricity. It is the impurities in water that actually make it highly conductive. When you start with very pure water (which is what you want to do) there is little in the water for the electrical current to pass through, so the process of producing colloidal silver starts very slowly.
As more and more silver begins to deposit in the water from your silver rods the conductivity of the water increases, which also increases the current flow. If this is not kept in check and limited to a certain range it will snowball into a runaway process with an ever increasing current that works very quickly but has to be very closely watched and stopped at just the right time to prevent it from "over cooking". This runaway process produces much larger silver particles in the water and has a tendency towards agglomeration, which is NOT a good thing to have.
A constant-current generator is slower in producing colloidal silver but it is much more forgiving (it's not as easy to "over cook") and should produce a better quality product with few worries or hassles.
If you are buying a colloidal silver generator make sure it uses some variation of Constant-Current output. Anything else is older technology that is not worth having and will not produce a quality product.