They are pretty much the same thing. 萌 is from Japanese '萌え'，Chinese started using it as 'cute' only since recent years.

可爱： this word used more broad in anything which is lovely. 萌： = cute+pretty/hasome a cute baby. a cute lady who is pretty , lovely and a little sexy.

Hello, That is such an interesting question. Haha, I find that I also strike myself into trouble when trying to distinguish them as a native Chinese. According to my search in our Chinese Internet, there are several resonable notions. Some people think "萌" is cuter than “可爱” when you deem someone or something cute extremely you have ever seen. While others think "萌" is the mixture of little stupidity and cuteness , with respect to the "可爱" used to describe someone‘s appearance is beautiful and exhilarating. Additionally, "萌" is relevant to the behavior of someone regardless of the appearance. I hope my answer will do you a favor~ If you still feel confused, please leave a message under my answer~