JTAG, SWD, EDBG, ICSP, ISP terms
Chipmakers have different names for programming interfaces that all basically do the same thing:


ISP - programming interface for Atmel (now Microchip) AVRs. SPI-like (MISO, MOSI, SCK, reset). It can be used for flash programming and debugging.
PDI - newer programming interface for Atmel AVRs (eg. Xmega). Uses two wires (data and clock). Can do the same as ISP.
DebugWire - yet another interface from Atmel (this one uses only a single wire)
ICSP - programming interface for Microchip PIC line of MCUs
SWD - Serial Wire Debug - programming interface for MCUs with ARM Cortex-M cores (uses two wires - data and clock)
JTAG - very generic term, SPI-like interface used for boundary scan, can also be used for programming/debugging MCUs (almost every vendor has its own protocol, so Cortex-M JTAG is not the same as AVR JTAG or Blackfin JTAG)
Spy-Bi-Wire - yet another two wire programming interface, this one is for TI's MSP430 MCUs


Finally EDBG that is explained here is most likely a debugger firmware that can run on one MCU (with USB) and debug another MCU (so that there are actually two MCUs on a development board). As you can see in the linked document it supports multiple Atmel programming interface standards.