SWDAP vs CMSIS-DAP vs DAPLink

CMSIS is the generic name for ARM-specified infrastructure around Cortex processors. The project we know today as DAPLink actually started as mbedmicro/CMSIS-DAP, we can find multiple references of the rename in the project history. "CMSIS-DAP" name became ambiguous as it was both the name for the spec and Mbed's implementation.

So today, CMSIS-DAP is the protocol, DAPLink is an implementation of this protocol.

CMSIS-DAP is not the most efficient debugger protocol in the JTAG/SWD world, but gets the job done at a (very) reasonable probe-side computing resources (i.e. entry-level MCUs with USB can run it, like cheap LPC11s). CMSIS-DAP is supported by OpenOCD and many other tools on the host side.

CMSIS-DAP specifies both JTAG and SWD commands, DAPLink provides support for both.

As DAPLink is an implementation with a permissive license, it can basically be used anywhere at no extra cost. Many different vendors create boards with DAPLink firmware on them, either alone (making a standalone probe like you linked) or alongside a target CPU (like we have on devboards). All hardware implementations of DAPLink embed the same firmware with the same functionalities, and you should be able to rebuild DAPLink and update them if needed.

Update after modifications from OP

CMSIS-DAP is defined in relevant document on ARM software page. You'll find all the details in Reference section.

LTek may name its boards as they want, even if name is somewhat misleading.

As I wrote above, all probes using DAPLink implementation as core firmware will provide the same set of functionalities.

As for the SWD/JTAG support, the only limitation you may have on some boards will be hardware: if manufacturers did not provide connections for TDI and TDO, you are out of luck to make JTAG work with them.

About SWDAP probe, ARM's own page states "The SWDAP is an open hardware design delivered as part of the mbed-HDK", that's why LTek is able to provide a verbatim clone.

DAPLink states that it uses the CMSIS-DAP protocol, which is supported by OpenOCD

CMSIS-DAP, as the name suggests, is a protocol and firmware developed by ARM - the company which designes the processor cores. The firmware itself supports both SWD and JTAG. http://www.keil.com/pack/doc/cmsis/DAP/html/index.html?_ga=2.84588765.557139549.1541455299-619225292.1541455299

Judging by the PCB labeling ("ARM University") the CMSIS-DAP probe is a reference implementation from ARM or their affiliate.