A water softener is a device which contains a resin to create an ion exchange to soften water. This systems use Salt of Potassium as part of the ion exchange.
A Reverse Osmosis or "R.O." as it is commonly called is a water purification device that uses a series of filters and a semi-permeable membrane to filter our water contaminants. They are used for drinking water and are usually located below the kitchen sink.
A soft water loop or "Pre plumb" for water treatment will typically be in the garage and will be a pipe that comes out of the wall and goes back in. It is common for it to have a smaller pipe attached in the middle of the square U shape.
Water Conditioners can encompass almost anything. They are units or media or chemicals to remove, reduce, or alter items found in water.
Water Filtration typically means using some type of carbon media in order to absorb chemicals resulting in a reduction or removal of chemical contaminants. Many systems can fall into this category, despite having different functions and purposes.
Salt Free systems can include things such as Reverse Osmosis, distallation, water filtration, water conditioning etc. Practically any system which does not use salt to facilite an ion exchange could be called a salt free system. They all have different functions and purposes so make sure you determine what your water issues are to ensure it will be properly addressed with your salt free option.