Although voltage testers and voltage detectors are different tools, their purposes overlap and they can be considered alternatives to one another. Both tools can show when voltage is present.
Voltage screwdrivers are like voltage detectors, in that they have a single point of detection. However, voltage screwdrivers require the hand to be in contact with the tool to complete and ground the circuit. Voltage screwdrivers are not thought to be as effective as voltage detectors because using your body to complete the circuit presents a risk for those without the electrical know-how.
Socket testers are devices that are used solely for checking that plug sockets are wired correctly. They are plugged into a socket and have a series of LEDs which indicate and identify problems. The socket tester is a helpful alternative to voltage detectors when testing sockets, but its single function means it cannot be used for other tasks voltage detectors are capable of, like checking for breaks in wires.
Voltmeters are the devices you may have used in school to test voltage. They are single purpose, give you a numerical voltage reading, and are used in the same way as voltage testers. Voltmeters however, are not widely available and a voltage tester or multimeter (see below) are often considered to be voltmeters, as they perform the same task.
Multimeters are versatile tools, as they combine the functions of other tools and can be used to measure multiple things. Multimeters measure voltage in the same way as voltage testers, and are more useful if you have other electrical checks to carry out.