I think the water is Jesus himself. So if it's Jesus himself then it's the same in both passages. Let's look at this verse from the epistle of John
6 This is the One who came by water and blood, Jesus Christ; not with the water only, but with the water and with the blood. It is the Spirit who testifies, because the Spirit is the truth. 7 For there are three that testify: 8 the Spirit and the water and the blood; and the three are in agreement. (1 John 5:6-8, )
We can see clearly that Jesus came by water and blood. So whenever we hear of water been personified in the New Testament, it's highly possible that it's referring to Jesus. And he also said that three testifies. The water, blood and spirit. And now we know that the Spirit is the Spirit of God or the Holy Ghost. The blood and water together is Jesus as I've said earlier.
The following verses clarify my point as the Holy Ghost as a seal
21 Now He who establishes us with you in Christ and anointed us is God, 22 who also sealed us and gave us the Spirit in our hearts as a pledge. (2 Corinthians 1:21-22, )
In Him, you also, after listening to the message of truth, the gospel of your salvation--having also believed, you were sealed in Him with the Holy Spirit of promise, (Ephesians 1:13,)
The testimony of Jesus is through His blood. That's he washed us and made us whole by his blood so that he can testify of our faith to the father. Let's consider the following verse which is kind of an analogy between Jesus and a godly husband
25 Husbands, love your wives, just as Christ also loved the church and gave Himself up for her, 26 so that He might sanctify her, having cleansed her by the washing of water with the word, 27 that He might present to Himself the church in all her glory, having no spot or wrinkle or any such thing; but that she would be holy and blameless. (Ephesians 5:25-27, )
Here too we can see the Water. And Jesus's work to testify before the father by the washing of the water.
RE: Jesus Teaches a Samaritan Woman