Exposed shower systems are mixer showers that need a hot and cold supply and all the workings are on the outside of the wall. The showers valves are normally thermostatic (which means that the temperature is constantly regulated & controlled in case of any interruptions to the hot or cold water supply). Manual showers are the opposite and don't have a constant temperature control.
They are favourable for solid walls due to their ease of installation on the outside of the wall as only the water supply pipes need chasing into the wall. Spare part cartridges are easily accessed by removing the handle/knob for maintenance. The majority are 150mm pipe centres for installation which means any model should be relatively easily replaced with any brand if a whole new system is wanted.
You can normally either have a single handset on a slider rail or a combination with a large drench head above as well.