In English, "the glass of the water" refers to a specific type of water, whereas "the glass of water" refers to any type of water, but I am assuming that there is no such distinction in the Greek ?
There is "the glass of water" that would be "το ποτήρι του νερού", and "the glass of that water"=το ποτήρι αυτού του νερού for specific water.