Hi Van, 

Thank you for this interesting question which I personally have been asked many times.

I like this explanation in French -

https://polyglottes.org/2018/10/17/billet-ou-ticket-choisir-le-bon-mot-en-francais/

 

and in English -

Billet and ticket are two words that are often used interchangeably in everyday language, but they actually have different meanings in French.
Billet refers to a piece of paper or card that grants access to a specific event, place, or service. For example, a train ticket, a concert ticket, or a museum ticket are all types of billets. In French, we also use the word billet to refer to a banknote.
On the other hand, ticket refers to a small piece of paper or card that is used as proof of payment for a specific service or transportation. For example, a bus ticket, a parking ticket, or a movie ticket are all types of tickets.
So, the main difference between billet and ticket is that billet grants access to something, while ticket is a proof of payment.
It's important to note that in some cases, the words billet and ticket can be used interchangeably, especially when referring to transportation. For example, you can say "un billet de train" or "un ticket de train" to mean a train ticket.
Hope this helps!