Saruman definitely didn't stay in Middle-earth - the Unfinished Tales say "[...] Curunír was cast down, and utterly humbled, and perished at last by the hand of an oppressed slave; and his spirit went whithersoever it was doomed to go, and to Middle-earth, whether naked or embodied, came never back".
It's different. The Silmarillion tries to tell the whole story from beginning to the end (heavily edited / retold by Christopher Tolkien); the Unfinished Tales select a few stories and give Tolkien's original text, which is more detailed than the Silmarillion, but also very fragmentary, and needs clarifying comments by Christopher Tolkien.