A content clause (also called a finite clause or an independent clause):

• expresses that a subject (person, place, thing, object, concept, etc.) takes action to do something, causes something to happen, or experiences or undergoes a change in state.
• functions as:
  • a simple clause. The leaves fell.
  • as a coordinate clause: The leaves fell and they blew away.
  • as a subordinate clause:
    • a subject. That the leaves had fallen was noticeable.
    • a predicate complement. We know that leaves fall.
    • the complement to a preposition in an adjunct phrase. They noticed the tree because its leaves had fallen.
• takes form as:
  • a simple clause:
    • with at minimum a subject and predicate. Wind blows.  [N + V]
    • with phrases (NP, AdjP, AdvP, PP etc.) and a predicate (VP) The wind   is blowing   the leaves.  [NP + VP + NP]
    • with complements—elements required by the subject and predicate to make sense. The boy put the leaf down. [NP + V + NP + PP]
  • a clause with dependents:
    • may also include adjuncts—nonessential element.  The wind blew the leaves on the ground.
    • may also include supplements—nonessential elements that are loosely related, expressing opinion or related to the speech act.  Perhaps, the wind blew them off. Frankly, I have no idea.  See Stance Adverbs.
  • a subordinate clause (also called "embedded clause")
    • a declarative clause, marked by that, which completes a thought. (e.g., know, think, agree, believe). I think that you are right. See Declarative.
    • a statement clause, marked by that, which embeds quoted speech. (e.g., say, admit, announce) in a statement. He says that you are right. See Statements.
    • an imperative clause, marked by that, which embeds an order or strong wish. (e.g., insist, order, tell) in a statement. He insisted that we clean up. See Imperatives.
    • a closed question clause, marked by if or whether, which embeds a question. (answerable by yes or no) in a statement; He asked whether the leaves had fallen. See Yes-No Questions.
    • an open question clause with an interrogative pronoun as the head of the clause—who, what, why, when, where, how—which embeds a question in a statement. He told me why they had fallen. See Wh-Question.

The name "content clause" differentiates this basic clause from the two other clause types—relative clause (modifying) and comparative clause (comparing).  (Huddleston 2 §10)

Modern grammar description separates: 

(1) function "what a word, phrase or clause does in a clause" (e.g., subject, predicate, modifier)  For example, the function of Subject can be realized by a noun, noun phrase, a gerund, an infinite or a clause.

(2) word category "what a word, phrase or clause is called" (e.g., Noun, Verb, Adjective, Adverb) This has also been referred to as "part of speech". The members of a particular word/phrase category share properties with other words/phrases in the same category.

Renamed Terms

• Adjective Clause is a traditional grammar term for a clause that modifies a noun. However, in modern description "Adjective" is a term reserved for the word category Adjective (Adjective Properties). The clause is a modifier (not an adjective) to the noun. For this reason, the clause is referred to as a relative clause because it relates additional information to the noun.  
• Adverb Clause is a traditional grammar term for a clause that modifies the verb. However, the adverbs (when, while, because, since, though, if , so, etc.) have been reanalyzed and moved to the category Preposition (Preposition Properties). The structure is now called a Prepositional Phrase (not a clause). See Connective Prepositions.
• Noun Clause is a traditional grammar term for an embedded clause that functions as the subject or "object" (predicate complement), of the clause in a similar way that a noun does. However, a clause is a structure; it cannot be a word, a "noun". (See Noun Properties).  For this reason, the structure is called a subordinate clause or content clause because it adds information or content in a complex form within a clause.

See The Cambridge Grammar of the English Language, 11 §3.1 and Longman Grammar Of Spoken And Written English, 2.13.