In British English, if a house has a yard it is a (usually small) area with a hard surface. To us, the Dutch 'tuin' translates to 'garden'. Indeed, online dictionaries tend to give 'garden' and not mention 'yard'. The "Open Tuinen Dagen" event website translates only to "Open Garden Days".
Nice to see that Duolingo accepts this, but a pity it isn't the main option. The rest of the world doesn't understand American yards.
It is not the same thing. In your sentence there is a large yard with the house, can be in front of the house, behind the house, next to the house, around the house. It is not specified.
- Om het huis - around the house, specifies that the yard is located around the house, and not for example only in front of it.
I think that Duolingo is using the American English translation of "tuin" here. In America, any area of grass or plants around a house is considered a yard. The American definition of garden would be more of a smaller, dedicated place for growing special plants like flowers or food plants. Put simply, a "backyard" is basically the same thing as a "back garden", so for an American English speaker the most correct translation of tuin would be "yard", but for a British English speaker the most correct translation of tuin would be "garden".