Many development and prototyping board platforms have specifically defined form factors that allow for quick expansion of capabilities, and often times these form factors are given names. Below are some of the more common expansion form factors with names - please feel free to add any that were missed.
Arduino - Shields come in the regular UNO style R3 variant and the larger Mega R3 variant. R3, or Rev 3, has become the defacto for Arduino and compatible boards today, and in addition to some other changes to the MCU boards, saw the addition of SCL and SDA pins next to the AREF pin, and an IOREF and another unused pin next to the Reset pin.
Raspberry Pi - HAT (Hardware Attached on Top) may come in either the older 26 pin variant or the newer 40 pin variant. pHAT (partial HAT) is a variant designed to match the form of the Raspberry Pi Zero and Zero W boards, but the pinout is the same between HAT’s and pHAT’s, so they can be used interchangeably. Another naming convention recently launched by Pimoroni is SHiM (Shove Hardware in Middle), which are low profile boards designed to fit between a Raspberry Pi and a HAT or pHAT and typically only utilize just a few of the GPIO pins. It should also be noted that the definition of a HAT by the Raspberry Pi foundation states that an EEPROM should be present on the expansion board with information about the board (i.e. manufacturer, GPIO map, etc.), though this is often omitted.
BeagleBone - Capes may be defined for use with a specific variety of BeagleBone, but this is usually defined by the features of the board rather than the pinout.
Feather - FeatherWings are add-on boards for Adafruit’s Feather ecosystem of MCU dev boards.
mikroBUS - click boards add functionality for MikroElektronika’s microBUS expansion platform for popular dev boards, such as Arduino, Raspberry PI, and others, and adapter boards are available for this purpose.