"What is the actual difference between a generic washing liquid, a wool washing liquid, ordinary soap, travel soap or showergel? Are the actual differnces? Or just a marketing gimmick?"
Good question! They very acording to how strong they are. A strong houshold detergent, say Tide for example, is strong enough to leach internal components of wool (and down) that make up the actual structure. Take an old wool sweater and wash it in detergent 10 times. It will get stiffer, and down right brittle. You can actually measure the strength of a fiber by simply pulling on it. The detergent has washed away the lanolin, a component of the fur that keeps it softer, more flexible and stronger. It is designed to break the bond between oils and substrate (other things happen chemically, of course.)
A body soap is generally quite strong, but not strong enough to do damage to your body. It is designed to STRIP oils from living skin. Like the Tide example above, it is designed to break bonds between oils and substrate. That's OK. You body replaces them. A wool sweater cannot.
A wool soap is not as strong. It is designed to loosen the bond between oils and substrate, but not break them. Think of this as a statistical curve, though. Some of the bonds are still broke. Rather than 10x washings, it might take 50x washing to notice any damage. It might take 100x washings to have a damaged garmet from washing. This is about the lifetime of any one garmet, anyway.
Down wash or similar is a weak detergent, or more of a true soap. It doesn't break the bonds between oils and substrate, it simply gives oils a different place to bond to, if it can. So, it doesn't was out lanolin, unless it is loose already. Good for removing body oils, but not removing the lanolin (or the same type oils in down.)
Travel soap or shower gell, is just another version of detergent. Hair detergent is quite strong, since it is designed to remove oils. Conditioners are usually mild detergents with some light dye like agents that will bond to open sites in a loose bond. Like fabric softeners, these are designed to fill in open bonding sites and prevent static and dirt from sticking with the side effect of making them feel softer, or, make hair not stick to itself. Sometimes they will leave a residue, themselves.
Water is a type of detergent that does the most for removing dirts from a garmet. Once the oils have been taken care of, water rinses the remainder away...dirt, etc. Water disolves everything to some degree. It has acidic and basic radicals in it. Water alone can cause some damage to wool(and down), indeed most stuff. Nothing you can do about that. It will also open bonding sites by "washing" out previously bonded things. Adding a bit of salt will increase this effect. All common detergents and soaps are designed to work with water. Only dry cleaning is a bit different.
A true soap is made from Fats and Lye. Detergents are MUCH better cleaners for most things, but, in many cases (wool, down, natural rubber, etc) are too strong and can actually damage the substrate material as they clean it.
Look up Soap vs Detergents in google.