Betel contains a spectrum of phenylpropene compounds which makes up a good part of the smell from the leaves. Eugenol is one of them and it causes your mouth to go numb. Eugenol is also found in other plants such as basil. There's also other chemicals such as chavicol, isoeugenol, and chavibetol.
Interestingly these chemicals can (theoretically) be used in the synthesis of psychedelic phenethylamines. A good example is safrole in the synthesis of MDMA. Plants are chemical factories.
Hmmm, interesting too. I do not have basic health sciences, but the use of these terms is totally incomprehensible to me. In Indonesia, especially in the province of Aceh, the use of betel leaf as a natural medicine based on the experience of its predecessors, so far I have found no obvious side effects, but chewing betel leaf is as you say "our mouth to go numb"