The annoying thing about this question is, since time keeps moving forward & consoles keep changing, we constantly have to redefine the eras that came before. Plus, there is no definitive cutoff between these eras since there's always a system that's ahead (or behind) its time.
For me then, at least, I tend to group things out by some quality that covers most of the major systems of the era, then add in whatever unstuck in time contemporaries those systems had. My head's landed on:
-systems pre-NES, which largely ran on f-plug/TV switches.
-post-NES cartridge systems, which (aside from carts) saw the rise of composite & the automatic RF switch. Plus the d-pad was standardized.
-CD based consoles, fairly self-explanatory there
-Internet consoles, which brought the idea of an always connected machine mainstream, as well as moving to HDMI as the standard connection.
Is it a perfect system? Of course not. There's always gonna be issues with the outliers- the N64 comes immediately to mind. I put it in the CD era, despite it being a cartridge system, becuase that's what the competition was.
As for where the cutoff from classic to modern is within those eras... right now, i put it in between cartridge & CD. You just don't see a whole of nostalgic excitement for disc-based machines yet. Keyword 'yet'- I think the Playstation's time is coming. Especially when the patents for these machines run out & clone units can come to market, increasing accessibility & awareness. First company to make a good multi-CD clone (ala retron 5, but without the shadiness) is gonna clean up!