A connector:

• is a general term for a word that joins a word, phrase or clause to another clause.  In traditional grammar, this is called a "conjunction". *Linguistic description reserves the term "conjunction" for the "coordinator" and.  (See Conjunction vs. Disjunction.)
• takes form as a coordinator (and, but, or) or a subordinator  (that, whether, if, to, for ), or a preposition (e.g., because, though, before, after, since, when, if [conditional], unless, as, than)

A coordinator:

• expresses a meaning of addition, contrast, or option.
• functions as a marker that coordinates like  (same kind or equal) elements or structures—two noun phrases, verb phrases, clauses and so on.
• takes form as: and (addition), but (contrast), or (option/alternative).  Some traditional grammar descriptions include for ( reason), so (result), yet (concession) in the category of coordinators. Linguistic description places for, so, and yet  with linking adverbs. 

A subordinator:

• expresses no particular meaning.
• functions as a marker for informational content placed within a clause. 
• takes form as:
  • that before a declarative clause; She says that she likes walking. She says [*just] that she likes walking.  Note that is often omitted in informal speech before commonly used verbs such as said, think, know, believe.
  • whether or if before a  yes-no question (closed interrogative) clause; He asked [whether/if we could go with him tomorrow.]
  • to before a bare (plain) form verb in an infinitival clause;  She wishes to [walk tomorrow.]  See Nonfinite Clauses.
  • for before a noun or accusative (obj) pronoun before an infinitival clause;  She wishes for [us to [walk tomorrow.]] Infinitive Cls w/Subj

An adjunct preposition:

is a preposition, which together with its complement, forms a prepositional phrase. The preposition connects the phrase to the main clause. The prepositional phrase is called adjunct because it adds information to the clause that is extra, not required to complete the meaning of the main clause. (We began walking because we needed exercise.)

(This connective is also called an adverbial preposition. The structure (connective + complement) is called an adjunct prepositional phrase (linguistic description) or an adverbial clause (traditional description). See Connector Overview for grammar source details.)

A prepositional head:

• is the primary word of a prepositional phrase.  It is called a head because of (1) its primary position (beginning) in the phrase → We walk [because we like walking]; or (2) its primary role (meaning) in the phrase→ We walk [only because we like fresh air].  In the case of a double preposition, it is the first preposition that is the head.  We walk inside of the park.  We can't get out of the house early.
• functions as the connector between the main clause and the phrase. It also relates the information in the phrase to the central idea of the main clause. 
• relates a phrase of: manner (in a hurry), timing (in the morning), location (on the sidewalk), reason (because, since, as), concession (though, despite), purpose (in order, so that), time-related (after, before, when, while, until), condition (if , unless), an expression (in a flash), comparison (than, as, of, from or to) and more.  The phrase is called adjunct because it adds information that is not required to complete the the main clause; it is extra.

• takes form as:
  • a preposition, such as in, on, at, over, before, after, while, because, though, until, as or than, which may take a complement of a noun phrase, a gerund, an infinitive, a full clause or another structure, depending on the meaning of the preposition: at home (N), in the house (NP), out of the house (PP), in stead of at home (NP+PP), after leaving home (Ger), rather than to leave home (Infin), because we left home (full clause). 
  • a comparative preposition—as, than, of, from or to—followed by a full or reduced clause. He walks as fast as I walk. He walks faster than I do. He walks the fastest of us all. He walks a different route from the one we walk. His route is similar to our route.) 
  • a conditional preposition—if or unless— followed by a clause expressing a condition. We walk [if we have time].
    (Yes, a prepositional phrase may include a clause.)

Also see clausal heads—who, when, where, why—(interrogative pronouns) that occur in embedded wh-questions. Similar to the phrasal head, the head of the clause is the connective and it carries meaning as part of the clause. She told me who is coming. She told me whom she invited__.  Subordinated Wh-Questions.