Both of these are compound complex sentences. In one, the first clause is simple ([§ 451]) and the second is complex. In the other, the first clause is complex and the second is simple.
CHAPTER II
ANALYSIS OF SENTENCES
SIMPLE SENTENCES
458. In analyzing a simple sentence, we first divide it into the complete subject and the complete predicate. Then we point out the simple subject with its modifiers, and the simple predicate with its modifiers and complement (if there is one). If either the subject or the predicate is compound, we mention the simple subjects or predicates that are joined.
1. The polar bear lives in the Arctic regions.
This is a simple sentence. The complete subject is the polar bear; the complete predicate is lives in the Arctic regions. The simple subject is the noun bear; the simple predicate is the verb lives. Bear is modified by the adjectives the and polar; lives is modified by the adverbial phrase in the Arctic regions. This phrase consists of the preposition in; its object, the noun regions; and the adjectives the and Arctic, modifying regions.
2. The polar bear and the walrus live and thrive in the Arctic regions.
The complete subject is the polar bear and the walrus. Two simple subjects (bear and walrus) are joined by the conjunction and to make a compound subject, and two simple predicates (live and thrive) are joined by and to make a compound predicate. Live and thrive are both modified by the adverbial phrase in the Arctic regions.