It’s quite understandable that you find that bit of Ruck confusing: it’s misleadingly put, and many people get confused about the distinction he’s making. And I doubt that you’ll find those b-greek posts very helpful. Here’s my attempt at explaining what Ruck’s getting at:
An example of a verbal noun is φιλία, “friendship” or “liking” or “love.” φιλία has a corresponding verb, φιλέω (be a friend of, love, like).
Now here’s the tricky bit:
φιλία μητρός (μητρός genitive of μήτηρ “mother”) could mean (1) “a mother’s love” as in “a mother’s love for her children”
or it could mean (2) “love of a mother” as in “the children's love of their mother.”
In the first case, grammarians classify the genitive μητρός as a “subjective” genitive. If the “loving” idea were expressed by the verb instead of by the noun, the construction would be μήτηρ φιλεῖ, “a mother loves (her children)”: the mother is the grammatical subject.
In the second case, the genitive is “objective.” μητέρα φιλοῦσι, “(the children) love their mother”: the mother is the grammatical object.
The labels are just a conventional way of defining the function of the genitive in a given context. In formal terms φιλία μητρός is ambiguous. But in practice the relationship of the genitive to the noun is usually clear from the context.
The genitive has a good number of other syntactical functions too (“possessive” is one, as in “the mother’s children”), and as you get further along in Greek you may find it useful to sort them all out.
I don’t know if you’ve reached the definite article yet, so I haven’t used it in my Greek examples above, but proper Greek would.
And finally, if this is too confusing at this stage, don’t worry about it. It will all make sense in time.
jeidsath, I do think your post would be better dealt with in the NT forum, so I’ll address it there.
PS @David, Yes τοῦ ὕδατος ἐπιθυμία is a straightforward example of an objective genitive, "desire for water." But if it referred to "water’s desire" for something, as grammatically it could, it would be a subjective genitive. But such labels are only for analytical purposes, and you shouldn't get hung up on them, as too many students do. It's best to see what the Greek means (which usually is not difficult to do) and then translate accordingly, rather than going by English translation. Once you learn how Greek works, you'll be able to dispense with translation altogether.