If we look at modern dictionaries chandelle and bougie are indeed sometimes given as synonyms and used as such by lots of people.
But strictly speaking bougies and chandelles are different objects, even if their purpose is the same.
If you have, at home, or at the restaurant, a dîner aux chandelles you are not likely to have dinner lit by chandelles but by bougies.
Chandelles (candles) used to be made of tallow (suif in French) and sometimes (rarely) from wax. Tallow doesn't burn well and smells bad when hot. Candles made of wax became more widespread in France from the 14th century onwards because they started to import great quantities of wax from the town of Bougie (nowadays Béjaïa) in Algeria. And that's when the word bougie began to be used for wax candles in France.
In Britain wax also gradually replaced tallow in candle making but English didn't change the name as French did.
So strictly speaking chandelle is a tallow candle, and bougie is a (wax) candle.
Note that candle and chandelle both originate in the Latin candela.