"Nintendo Wi-Fi Connection" means that you're able to play it online using Nintendo's WFC (Wi-Fi Connection) service.
"Wireless DS Single Card Download Play" means you can play with other plays that don't
have the game but can "download" a demo sort of version of your copy to play multiplayer with you.
"Wireless DS Multi-Card Play" means that you can play the game multiplayer with others that also have their own copy of the game.
And yep, Nintendo Wi-Fi Connection is their online service name