A compound sentence contains two or more principal clauses.
A complex sentence contains one principal clause and one or more subordinate clauses.
A phrase is a group of related words used as a part of speech. (See [Exercises 68] and [69].)
A clause is a group of words containing a subject and a predicate. A subordinate clause is used as a part of speech. It usually has an introductory word to distinguish it from a principal clause. (See [Exercise 71].)
Illustrations
Simple sentence: To-day most of the world's big questions are business questions.
Complex sentence: The view that business is only humdrum routine and sordid money-making needs revising, since most of the world's big questions are business questions.
Compound sentence: Many people still belittle business, calling it humdrum routine and sordid money-making, but this view needs revising.
Phrase: (a) of the world's big questions.
(b) calling it humdrum routine and sordid money-making.