A NTP server is really just a time server that utilises Network Time Protocol (NTP). Whilst other time protocols do exist, NTP is by far the most commonly used and is utilised in over ninety percent of time servers.
NTP server and time server are therefore interchangeable terms but describe the same thing: a device used to receive and distribute a timing signal.
The timing signal utilised by most NTP servers is a UTC time source. UTC (Coordinated Universal Time) is a global time scale based on the time told by atomic clocks. By utilising UTC a NTP server can in affect, synchronise a network to the same time as millions of other computer networks from around the world. This has made possible many online global transactions that just simply wouldn’t be possible without UTC.
The timing signal is received by the NTP server (or time server) via a number of ways; the Internet, national time and frequency transmission (long wave) or the GPS (global positioning system) network. Once received the time server (NTP server) checks the authenticity of this signal (except from Internet sources where authentication is not possible), evaluates its accuracy then distributes it amongst the network.
To prevent a possible overload of time requests to the time server, machines that receive a time signal from the NTP server, can themselves be used as a time reference and the machines that receive a time signal from those can again be used as a reference. This hierarchy is called stratum levels. A NTP server is a stratum 1 device, a machine that receives a signal directly from the time server is a stratum 2 device and if a machine receives a signal from that it becomes stratum 3.