Thank you for pointing this out. 

To the OP. How about adding "Games" here...

I still can't vote, because "Games" isn't an option. I mean... We weren't dumb enough to call Genesis games Nintendo games, even though I appreciate the jab. 

So following that logic, an 8track =cassette 
atari/nes/ etc= cartridge 
is it possibly a bad interpretation? Like cartridge is the same as cassette in Japanese?
 

Cassette has always meant "little case." It's derived from case and casket, which are usually rectangular containers. It means more than just audio cassettes. There's also gene cassettes and cogset cassettes for bicycles, neither of which involve analog tape.

Cartridge originally meant "roll of papers." It caught on for firearms as gunpowder was originally kept in a roll of paper. Cartridge as a container in general is much more recent, definatly more recent than cassette.

Either is perfectly fine for calling a circuit board within a plastic container.

Damn,Tulpa! Hit em with the knowledge! 
 

If you wanted the poll to be 100% stereotype accurate, the last entry would say "We just called them "Nintendo games", even for the Sega.", but good on you for actually using Genesis.

What about bike cassettes? Can you call that a tape?

And I feel weird calling a cartridge a "game." Consider a downloadable title that has a physical release. You can have the game installed on your system without having the game? the "game" is the software.

Not all cartridges are even games to begin with. Some are painting programs, or web browsers.

I have a bunch of Atari Starpath Supercharger games that are actual cassette tapes. Talk about a weird way to play Atari games.

Yes, the manuals for the Ultra Games releases not only use the "cassette" terminology but also refer to the NES as a "computer".
 
Perhaps from the perspective of a younger person but it was very common back then for computer games (Atari, Commodore, etc) to be sold in the tape format, especially in Europe where disk drives were rare and expensive.  The Starpath games are indeed unique in the Atari 2600 library though.
 

I was clearly referring to Atari 2600, but sure.  

In The Netherlands Nintendo called them "spelcassettes" which translates to game cassettes.

I'm pretty sure the term "compact cassette" was a trademark name for cassette tapes when they were introduced as a replacement to the old bulky 8-track cartridges back in the 60's.

Imagine the alternate universe where you pop a tape cassette into your NES, like it was a C64, and then the mini ones for your Game Boy.

'Tender tapes. Anything else is categorically incorrect.