The matter is simple - like the spoon from Matrix, the washing liquid (for dishes or floor) does not exist - or it does; you can always imagine it's already spilled on sponges and all dirty surfaces - which means that you can clean everything just like that. Simple division here:
- walls, sink, tables, shelves and everything above the floor, you wipe with sponges
- floor can be wiped only and exclusively with the mop.
In addition, probably all stains can be removed by simply pouring water on them, which is quite an interesting solution - even if you pour liters of water on the floor, you can't slip, and won't be nagged.
The game has a "soap" over the sink, but the developer confirmed it can't be used for anything else than a tasty addition for meals - so if one day, after a patch your magical sponges stop eating dirt, you'll know where to look.
There is another question about cleaning dishes, pans, and trays - more info about these pleasures you will find in the chapter How to work effectively?