Translation:My grandmother passed away the day before yesterday.
There are a lot of ways "to die" in Japanese, indeed, some of them are quite situational, many quite poetic or literary, so don't be surprised if you stumble into even more. And yes, for the most part they only differ in the "level of bluntness".
For example this one, 亡くなる, literally means "to turn into nothing" or "to become nothing". As an added bonus, it is another one of those expression that can also be used with the honorific prefix: お亡くなる.
I'm confused - this sentence means my grandmother died the day before yesterday - the same sentence that you say you had previously - if this is the case then it is not a case of "both" - they are the same sentence. fyi some duo lessons pretty much repeat the same sentence over and over and over again so having the same sentence repeated over two lessons (if that's what you're saying) is actually preferable to lessons that repeat one sentence over and over, in my opinion anyway. At any rate - it's free! Enjoy learning! :D
Gotcha! : ) I just did a few german lessons maybe yesterday that had the same sentence repeatd 2 or 3 times and also had the same sentence repeated but required you to translate it into English, or into German or write what you heard or choose the write words from a word bank - same lesson. arrrgghh. But free, so... ; )