The bottom line is this: Technically speaking, either form of colloidal silver – ionic or metallic – work. Both have powerful antimicrobial qualities.
But...in order for the metallic form of colloidal silver to kill pathogens it has to undergo a gradual conversion process inside the human body. It has to come into contact with acidic bodily fluids or highly oxygenated tissues and then start shedding silver ions, which are what actually kill the bacteria.
On the other hand, when you ingest the electrically-generated ionic form of colloidal silver no conversion is necessary. It's ready to work immediately because it's already in the biologically active, infection-fighting state.
In short, both of them work just fine.
But the metallic form (i.e., the so-called "true colloidal silver") works much slower, and far less efficiently, because the tiny bare metal particles it's composed of are inert (i.e., have no antimicrobial activity on their own) and have to undergo that gradual conversion into silver ions inside the human body before they can even begin to work against pathogens.
For further documentation, see this article from Rice University researchers demonstrating that the metallic (i.e., nanoparticle) form of silver is biologically inert, and cannot kill pathogens unless it sheds biologically active silver ions.