The game is normally buy to play, meaning you need to do a one time payment for the base game, after that there are no payments for the base game.
There is an optional subscription which gives you some small benefits and ease of life bonuses as well as access to all DLC packs whilst subscribed. This is more like a traditional MMO system.
You can purchase DLC seperately from the in game Crown Store rather than having a subscription if you prefer a buy to play and traditional video game style purchase system.
The current week lets people log in without that initial payment but they will have to buy the base game after the end of the event.