>Can you elaborate on that one?
I guess, but I don't know what more there is to say. Really, uses of know can be divided into three main categories: genitive particle, form of the copula, and verb nominalizer, but the third one isn't easily confused like the other two are because it's used in different environments.
The other two are more confusing because they both occur between two nouns or nominals, and have similar functions in that they both cause the first noun to modify the other in some way. However, they are distinct in exactly the meanings they convey and the syntax they allow.
The genitive particle is used when the first noun is used to express an attribute of the noun or a possessor of it. In English, this corresponds to the constructions [noun] + [noun] (attributive noun), [noun]'s [noun] (possessive construction), or [noun] of [noun]). As a case particle, the genitive particle, like other noun particles, is attached only to the head noun of a single noun phrase, i.e. the syntax is always [[NPの]NP], one NP marked by の that is an adjunct to a parent NP.
On the other hand, there is the の that is an attributive form of the copula (だ). To start, it must be acknowledged that な already exists and is usually acknowledged as "the" attributive form of the copula. In fact, の and な are allomorphs, i.e. they serve the same function and are in complementary distribution. The rules for when to use them are:
>before the nominalizer の, and any of it's phonetic reductions, only な is used for all cases. This is most often seen in the のだ construction, where both nouns and な-adjectives (and also の-adjectives) use the form な.
>otherwise, な is only used for the attributive form of な-adjectives
>in all cases besides before the の nominalizer, nouns (and の-adjectives) use the form の as the attributive form of the copula.
This can be made clear by both the syntax and the meaning of certain clauses that end with の. For example, I took the following sentence and translation from ejje.weblio:
<When I was a child, my mother gave me that book
First of all, look at the syntax. 私が appears to be a subject within the 時 clause. We may try to say that this is actually the subject of the overall sentence being forwarded to before the 時 clause, but the subject of くれた is 母が, therefore it is unambiguous that the clause 私が子供の時 has a subject and that subject is 私が. However, the presence of a subject requires the presence of a verb(al predicate). We could say that the subject is an omitted だ, but then it makes no sense for a の to come between (an omitted) だ, which is a verb, and a noun like 時, so の must be the verb itself.
This is supported by the meaning of the sentence. The translation is "When I was a child", or more literally "(at) the time that I was a child", which contains "I" as the subject of "was" (a copula) within a relative clause (which are the most direct equivalent to Japanese attributive clauses).