In both texts, one thing is perfectly clear - it is not literal water that is being spoken of. Jesus was using 'water' as a metaphor for something else, but because literal water does, indeed, sustain life, it was a perfect illustration of what people had to do to get spiritual life. Without literal water drunk by people, death will result in a few days. Continued life depends on a supply of water. And it has to be water that is not poisoned, or thick with salt (as in the Dead Sea). Living water stands in opposition to contaminated, death-dealing water.
In John 7:38 the word for water is 'hudor' and it means a colourless, transparent, odourless compound of oxygen and hydrogen in liquid form. John used that word 23 times in his Gospel - not that he would have known anything about it being comprised of oxygen and hydrogen!
John used exactly the same word, 'hudor', when he wrote Revelation 7:17. However, in both texts it is the prefixing of the descriptive, qualifying word 'living' that makes all the difference, and which connects both texts together.
The word 'zao' means 'to live', and is used in both texts. It speaks of that which is alive, as in Rev.7:2, '...having the seal of the living God'. Jesus described himself with that same word when he said 'I am the living bread... (John 6:35).' Just as Jesus was not speaking of literal bread, he was not speaking of literal water, nor was John writing about literal water in heaven.
Further, in the Revelation text, we learn that there is a fountain of this living water. The translation you quote says "springs". The fountain is the spring from which the river flows. In Rev.7:17 the word 'pege' is used, and it means 'fount, source'.
Perhaps the one difference between the two texts is that in John the Holy Spirit has to give this living water to people still on earth if they are to start living spiritually, whereas in Revelation Christ leads those who are already in heavenly glory to the very source of that living water. That source is the author of living water, the originator of it, and we know that God is the source of all life. As the Psalmist said, with God "is the fountain of life" (Ps. 36:9).
This makes for an interesting link between the Holy Spirit being the giver (bestower) of that living water to all on earth who would be brought to spiritual life; Jesus who is, in himself living water, and how he leads those in heaven to the very source of that eternal life which they freely partake of; and God being that source. Jesus said that, "As the Father has life in himself, so he has granted the Son to have life in himself" (John 5:26 cf. Deuteronomy 30:20, 'for the Lord is your life'). This is living water, indeed!