Aren't SD cards and cartridges different? I thought that cartridges used ROM while SD cards can be written to.

From a user standpoint, when we speak of "cartridge" we're talking about the packaging - 8-track tapes were also called "cartridges". Calling any game cart "ROM" has been a little bit off in that old cartridges were PCBs that could contain arbitrary chips, custom hardware, battery-backed RAM, etc.

With the modern carts, it's all flash memory - both the game binary and any user data can coexist. That said, it's much less common than in the NES era, but not unheard of, to incorporate custom hardware on the cart. For example the DS Game Card[0] has an infrared variation. With this change the overall performance model now is guided around working with flash memory - you have big mass storage, longer load times, and don't get to do any fancy bank-switching tricks or rely on an additional co-processor or an extra RAM bank.

[0] https://en.wikipedia.org/wiki/Nintendo_game_card#Nintendo_DS...