Here's a little list of typical laundry detergents and a translation. It's not meant to be an exhaustive list, but might be helpful as a starting point:
"Surfactants":
These could be anionic (negatively charged) or non-ionic (neutral) synthetic surfactants, in the form sodium-hydrocarbon-sulfate (or sulphonate). SDS or Sodium dodecyl sulfate is a very common high sudsing synthetic surfactant. (Tidbit: most fabric softeners are simply long-chain cationic (positively charged) surfactants)).
"Water Softener":
In a powder, this is typically washing soda, soda ash, or sodium carbonate (all the same thing). It's very alkaline and greatly aids "detergency", but it's main drawback, besides being harsh, is that it also forms a precipitate with hard water minerals in the water or in the soiled fabric. A much better water softener is complex phosphate (STPP) which doesn't form a precipitate. Both these types of softeners aid detergency by "breaking" soil from the fabric, and also by saponizing oils and greases (turns them into soap) by dint of their alkalinity. Another water softener that is popular in european detergents is zeolite, which is basically alumino-silicate. This softener traps hard water minerals within its microscopic labrinths, but it does nothing to increase alkalinity or break soil from fabrics.
Washer protection agent: Typically this is sodium silicate (any number of slightly different forms). It helps keep the precipitates formed by sodium carbonate from depositing and forming a harmful, hard crust on washer parts.
Anti-soil redeposition agent: Phosphate-free detergents typically use caroboxymethylcellulose (CMC) to help keep soil and soil-softener precipitates in suspension so they won't be redeposited back onto the laundry, but rather be rinsed away. My understanding is that this substance works ok, but not as well as avoiding the precipitate in the first place (as could be done by using complex phosphates).
Optical brighteners: Basically this is a dye that is invisible, but it will absorb near ultraviolet light rays and re-emit white light. So it makes whites look whiter. Its main drawback is that it can give the appearance of fading to dark colors. And being a synthetic dye, it is probably toxic.
Enzymes: Typically these are encapsulated (for less allergic reaction to detergent dust) enzymes that digest oils ("lipase") and proteins ("protease"). These in turn help to break down oil and protein based stains from fabrics. It is unclear to me if the proteases are safe, or not, for wools, silks, and leathers. When in doubt, use an enzyme-free mild detergent or hand soap for these fabrics. Also present may be cellulases, which can chew away at tiny fibrils of cotton, thereby reducing pilling on cotton and cotton blend fabrics. It is unclear to me if cellulases also shorten the life of cotton fabrics - my assumption is that the cellulases act primarily on frayed ends, not on the main fibers. Perhaps wishful thinking.
"Surfactants":
These could be anionic (negatively charged) or non-ionic (neutral) synthetic surfactants, in the form sodium-hydrocarbon-sulfate (or sulphonate). SDS or Sodium dodecyl sulfate is a very common high sudsing synthetic surfactant. (Tidbit: most fabric softeners are simply long-chain cationic (positively charged) surfactants)).
"Water Softener":
In a powder, this is typically washing soda, soda ash, or sodium carbonate (all the same thing). It's very alkaline and greatly aids "detergency", but it's main drawback, besides being harsh, is that it also forms a precipitate with hard water minerals in the water or in the soiled fabric. A much better water softener is complex phosphate (STPP) which doesn't form a precipitate. Both these types of softeners aid detergency by "breaking" soil from the fabric, and also by saponizing oils and greases (turns them into soap) by dint of their alkalinity. Another water softener that is popular in european detergents is zeolite, which is basically alumino-silicate. This softener traps hard water minerals within its microscopic labrinths, but it does nothing to increase alkalinity or break soil from fabrics.
Washer protection agent: Typically this is sodium silicate (any number of slightly different forms). It helps keep the precipitates formed by sodium carbonate from depositing and forming a harmful, hard crust on washer parts.
Anti-soil redeposition agent: Phosphate-free detergents typically use caroboxymethylcellulose (CMC) to help keep soil and soil-softener precipitates in suspension so they won't be redeposited back onto the laundry, but rather be rinsed away. My understanding is that this substance works ok, but not as well as avoiding the precipitate in the first place (as could be done by using complex phosphates).
Optical brighteners: Basically this is a dye that is invisible, but it will absorb near ultraviolet light rays and re-emit white light. So it makes whites look whiter. Its main drawback is that it can give the appearance of fading to dark colors. And being a synthetic dye, it is probably toxic.
Enzymes: Typically these are encapsulated (for less allergic reaction to detergent dust) enzymes that digest oils ("lipase") and proteins ("protease"). These in turn help to break down oil and protein based stains from fabrics. It is unclear to me if the proteases are safe, or not, for wools, silks, and leathers. When in doubt, use an enzyme-free mild detergent or hand soap for these fabrics. Also present may be cellulases, which can chew away at tiny fibrils of cotton, thereby reducing pilling on cotton and cotton blend fabrics. It is unclear to me if cellulases also shorten the life of cotton fabrics - my assumption is that the cellulases act primarily on frayed ends, not on the main fibers. Perhaps wishful thinking.