Short version: it does.
The first difference is that the fridge has a small, enclosed volume of air that it cools. There is a pretty limited amount of water vapour in the fridge to be condensed out at any time. Once it is all gone, there is no more until the fridge door is opened to let some new air in (although only some of the air will be replaced each time). The volume of air in a fridge is unlikely to contain more than a gram or two of water (a few cubic centimeters at most).
The AC on the other hand has an effectively unlimited source of water vapour.
Water that condenses out within the fridge can go on to the inner surfaces of the fridge, but can also go on to items in the fridge (and thus get taken out when items are removed). Some cardboard containers in my fridge are noticably damp when I remove them. Milk containers usually have some water condensed on them.
I've no idea whether vegetables or fruit in a fridge can account for absorbing some of the water vapour (equally they might be a source of water vapour) - they are a possible confounding factor.
Basically, the rate at which new water vapour is added to the fridge via the door opening is pretty low, and removing items from the fridge is likely to be a net removal of condensed water from the fridge, so the reservoir of water vapour condensed into liquid within the fridge at any time is pretty small, and when spread over all the potential surfaces and objects within the fridge, is not that noticable.
Plus every fridge I've ever had has also had a small drainage hole at the back of the compartment (the back wall being the coldest), although I've no idea where it drains off to.