Lewis and Tolkien were friends and contemporaries but the stories are different and separate.
Both were devout Christians and both stories have a distinct leaning toward Christian principles if you look at what they considered good and evil. Both are epics that bring in new characters as you go, both are about a journey and battle...and both have a lot of different beings and mythical creatures.
As for the differences, when Tolkien was asked about what his story meant, he refused to answer. He left that entirely to the reader instead of verifying that there was any symbolic commentary on Christianity, OR war OR any aspect of social/political climate of the time...in fact, he vehemently denied that his work was "really" about anything other than just being the story he gave us. However, Tolkien did realize that people would make these applications and was OK with it.
Tolkien was a language professor, I think at Oxford University. As such, he loved words and how they came to be and LOTR was created only after the Silmarillion and other works that laid the foundation for what Middle Earth was all about, who the people were, what they were like, he gave them maps and languages and histories and religions, etc. The reason perhaps that LOTR stands out as his most popular piece is because it is prefaced by an alluring story (The Hobbit) and you want to know more about the Ring...as well as being about how Middle Earth came into the Age of Men, and what we did to earn that responsibility, given the type of people we can be. LOTR didn't initially paint mankind with a very happy brush, you know. We were seen as greedy and addicted to power and there was a great deal of question on Middle Earth, especially among the elves, whether men would be able to handle things after the elves passed through. I don't know if Tolkien meant it this way, but many readers find themselves pondering the question as Aragorn took the throne at the end of LOTR, hope notwithstanding, "What are you going to do with your responsibility as a human being?" But enough on that.
Tolkien's work, then is a HUGE rich tapestry that brought an entire place to life with such detail it's hard to remember that it is all fiction. Parts of Tolkien's work reads like scripture, and he writes with a historical authority that makes you believe Middle Earth was real.
CS Lewis on the other hand and the Narnia books, is known as a Christian author and Christian literature. CS Lewis discussed his work and did not deny that the message of Narnia was distinctly Christian allegory with direct symbolism between the two. Aslan=God, Stone Table=cross, White Witch=Satan. Further, there were distinct ideas that were "on purpose": forgiveness, sin, resurrection, grace, faith, innocence of children.
Narnia fits into Lewis' body of work, most of which was Christian philosophy. He applied a lot of logic to Christian ideals and explained his faith this way, it is very highbrow thinking.