There is some debate about this, but potting mix, potting soil and potting medium are often the same thing with different names. The irony is that good potting soil is really a "soiless" combination of peat or coir, pine bark and vermiculite or perlite, none of which provide any nutrition to plants. However, these mixes are designed to stay "fluffy" and not compact too much in the challenging environment of containers. A good potting mix won't dry out too quickly, but will resist compacting so that the plant's roots can take up water and moisture from the surrounding medium. The roots must also have access to oxygen, which means the mix can't be too dense.
Some potting soil or mixes also container fertilizer or water retaining crystals.
Potting soils/mixes also come in different types. There are specific mixtures for succulents, orchids, roses, acid-loving plants and seed starting.More info on potting soil from Proven Winners