Our colleague Marcombes has correctly identified the technical difference between a connector (often used externally to equipment, for connecting it to the outside world) — e.g. a plug and socket — and a header, which is often used for internal interconnections
within a piece of equipment; in this role, it is flimsier than most connectors, as it is not intended for constant pluggin and unplugging, and also usually smaller, since space-saving is important, while a high degree of mechanical strength is not required. These things are often used with 'jumpers' that can be used to perform certain hardware configurations.
The problem is, these headers are usually male 'pin' headers, soldered into a PCB, and what plugs onto them is usually a female plug, typically mounted on a ribbon cable. My only qualm, therefore, is whether we can legitimately use header for both the male and female parts, irrespective of which one is fixed and which flying.
Here is a web page that shows various examples of 'headers' in use:
https://learn.sparkfun.com/tutorials/connector-basics/pin-he...You can see that they are really one special type of 'connector'.