There is an important distinction in that, due to the way computers access each form of media
The distinction here is between word-addressed and block-addressed memory. Cartridges were more often word-addressed, but it isn't quite a reliable predictor of this. TG16 "cards" were word-addressed and allowed execution in place. Nintendo 64 and Game Boy Advance "cartridges" had seek-and-read protocols, which were a compromise between word-addressed and block storage but allowed execution in place through caching (N64) or lots of wait states (GBA). Later systems were more likely to use block devices because RAM had become so cheap and block devices require fewer pins on the connector.
Cartridges could include hardware that extends the capabilities of the console such as the SuperFX chip, while Cards simply contain the game data and player's save data.
The "system cards" used with the TurboGrafx-CD expand the TurboGrafx-16's capabilities. And any SPI peripheral can be put on a DS Game Card. Most often it's used for a serial flash memory for save data, but the Pokemon HeartGold and SoulSilver Game Cards for DS also include an infrared transceiver for communication with a "Pokewalker" pedometer that the player uses to take one of his party members on walks.
In practice, there is also the distinction in that cartridge based game consoles expected a cartridge to be there, and there were no user operations permitted without one being inserted.
If no Mega Cartridge or Sega Card was inserted into certain revisions of the Master System, the player could launch the built-in Snail Maze game by holding Up + 1 + 2.