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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.

If we look at modern dictionaries chandelle and bougie are indeed sometimes given as synonyms and used as such by lots of people.
Nevertheless the use of the word varies according to French speaking countries. The BDLQ (Québec Board of the French Language) confirms what @gdupras says in their comment:

si en Europe chandelle est peu utilisé, au Québec, c’est un mot encore bien vivant, que l’on trouve tant dans l’étiquetage que dans les dictionnaires québécois comme synonyme de bougie. Ainsi, on ne saurait en déconseiller l’emploi¹.

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.

^{1 if in Europe chandelle is little used, in Québec it is a word still very much alive that is found both in labelling and in Québec dictionaries as a synonym of bougie. Thus we do not discourage its use.}

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.

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.

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.

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.

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 candle.

Note that candle and chandelle both originate in the Latin candela.

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.

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.