Mixer showers are one of the most common types of showers in the UK - from homes to hotels, many are fitted with mixer showers. But there's a bit more to a mixer shower under-the-hood.
A manual mixer shower allows you to adjust both the temperature and flow rate. Manual valves offer a high level of temperature control, but if the cold water supply is reduced (by turning on a tap or flushing the toilet, for example), the temperature of the shower will change, and could be either freezing cold or boiling hot depending on the circumstances. You will therefore have to manually adjust the temperature to compensate for this change as it happens. We wouldn't recommend manual valves to a household with children, elderly, or the less able, as there is a scalding risk if the water gets too hot unexpectedly. Manual variants tend to be less expensive than thermostatic mixer showers, and usually have a simpler use of operation.
A thermostatic shower houses a thermostat in the shower that controls the temperature of the water automatically. This means that if the temperature of the incoming water changes (by turning on a tap or flushing the toilet, for example), the shower will compensate for the changes and keep the temperature stable and constant for you. No manual adjustment is required by the user as the shower can adapt to the water change itself within seconds. Additionally, if the cold water fails (either a blockage or similar), the shower will shut down to prevent the risk of scalding. More and more modern mixer showers tend to be of the thermostatic variety.
A pressure-balanced mixer shower, as the name implies, compensates for changes in water pressure. It has a diaphragm inside the product which reacts to pressure changes, therefore maintaining the temperature. These showers are effective when you have changes to pressure (by turning on a tap or flushing the toilet, for example), however they aren't effective if the temperature of the water changes (such as when the hot water abruptly goes cold). In which case, the shower will not adjust the temperature as the pressure hasn't actually changed.