They are exactly the same. They are always interchangeable. You can say "this elephant is friendler than that one" or "this elephant is more friendly than that one". You can say "compared to the other elephants, this one is more friendly" or you can say "compared to the other elephants, this one is friendlier". Even when you repurpose the adjectives as nouns, the two expressions work alike: "Babar is the friendlier of these two elephants." "Babar is the more friendly of these two elephants."

Both "friendlier" and "more friendly" are correct, but they are used in different contexts. "Friendlier" is the comparative form of "friendly" when comparing two things. For example: This dog is friendlier than that one. "More friendly" is used when comparing more than two things. For example: Among all the dogs in the neighborhood, this one is more friendly. In general, when comparing two things, you can use the "-er" ending (e.g., friendlier, faster), and when comparing more than two things, you use "more" before the adjective (e.g., more friendly, more beautiful).