The fixed flange tow bar is the classic UK style of tow bar which has a fixed faceplate to which a tow ball (either standard or "Alko") is bolted.
The bar is permanently mounted on the car and this type can have older types of stabiliser brackets fitted. Lowering plates and bumper protector plates can also be fitted along with bike carriers that allow the car to tow at the same time.
This is still the most widely produced type made in the UK and usually the cheapest option.
This type of tow bar is permanently fixed and does not have the options of being able to fit plates, as with the flange type, and the tow ball height is therefore unable to be adjusted if required.
Perhaps less obtrusive on modern car design, a swan neck tow bar usually has electrical socket mounting well down the "neck" of the bar and has for years been the type most used on the continent.
It is compatible with "Alko" couplings. Swan neck tow bars are usually slightly more expensive as the widest ranges available are from the European tow bar makers.