I don't really know for sure what "non-biological" means. All automatic washing powders are enzyme based, and had been for years before the Bio and non-Bio distinctions appeared. My recollection is that one of the manuacturers (Lever/Persil) introduced an additional enzyme at one point which got them bad press because it was rather too over enthusiastic and treated some dark dies as dirt, and in its effort to get the 'dirt' off, wrecked the fabric fibres, leaving holes behind. When the reason for this came to light, all sorts of people started claiming skin problems too. Eventually they started producing the previous formula again under the "non-Bio" name, but AFAIK, all (European) automatic washing powders are enzyme based, and were for donkey's years before this incident too.
There was another problem in that consumers didn't reduce their wash powder dosing when the manufacturers upped the concentration. This resulted in much larger traces left after rinsing, and that was probably the main cause of skin complaints. However, if you're the market leader in a competitive market, you can't argue with an enraged customer base who were demanding the previous formula back again, and that's probably the main reason we now have the two types.