On the GBC then I am not sure I can call it a different machine that easily. For marketing purposes and in the eyes of many they would see it as such, however if it was mainly marketing than informed that...
http://bgb.bircd.org/pandocs.htm for the specs. Other than the homebrew one on the GBA then basically every emulator, programmer, hacker and such treats them as spins on the other.
It might have had exclusive games but there were still loads developed with backwards/cross compatibility in mind during the time. Old versions of GB games were enhanced and rereleased for it, several of those you could still have played on the original form though.
GG vs master system was more of a blurring on the lines thing for the purposes of this discussion. Going by intent there was not a lot pushing the Master system on GG thing, compared to the GBC stuff above where devs clearly intended many different people to play in all sorts of ways. That said what about the Sega Nomad?
There are no commercial PSP games but there are homebrew titles that are exclusive to various models, though I won't count the PSP1000 IR port stuff. Also the browser and AV cables (fairly radical for a handheld at the time).
Extra chips do still exist. The likes of the supercard DStwo/ismm/iplayer for one, theoretically the DSX could have had something, lots of flash carts kicked DLDI calculations to the carts, DSserial, the pokewalker on the DS stuck an extra communications bus on the save bus (
http://problemkaputt.de/gbatek.htm#dscartunknownextras ).
I can count the wii as a different console far more easily than the GB to GBC. It came with a whole raft of improvements, a retooled control system, something resembling a modern approach to security/OS design, a coprocessor and more. There are many things that lead me to label it an overclocked gamecube but that is more for when I am/was trying to get people to look at it for ROM hacking and homebrew purposes should they already be versed in the gamecube. No games were done for dual purposes that I saw, give or take Zelda TP but that saw dual releases anyway.
Interesting times are definitely ahead. The thing I will look to so as to differentiate them though is can I run my own software, almost* unfettered at that. Likewise constant upgrading became a bit passe some time during the PS360 era. As games hung back for consoles the specs wars kind of dried up and I could play games quite happily on years old machines, to this day a lot of things still do that or maybe that and a graphics card that goes for less than a game in many instances.
*unfettered in as much as while the new uefi stuff troubles things I can still run an OS, while the microcode is interesting it does not bother me and while the BIOS may be closed source for almost everything peh really.