Is parchment paper different from baking paper? If so, how?
Parchment paper and baking paper are the same thing. The terms are used interchangeably. It may sometimes also be called bakery paper.
Regardless of the name used, it can be either brown or white. Uses are the same - usually to line pans when baking or to cook foods en papillote.
From MetsaTissue , which is headquartered in Finland and sells primarily to European countries:
Grease proof papers are highly hygienic and heat resistant papers which enable a wide variety of uses.
Baking paper – also known as bakery paper or parchment paper, as it is often called especially in the US – is grease proof paper that is used in baking and cooking as it provides a heat-resistant, non-stick surface to bake on.
"Parchment" was historically used to refer to a prepared animal skin, so in some areas, either "baking paper" or "greaseproof paper" is the preferred term. I've also seen that some people specifically qualify it as "Baking Parchment"
For other differences between English dialects, see Translating cooking terms between US / UK / AU / CA / NZ
This particular one is towards the end under "Tools / Equipment / Non-food items "... currently:
parchment paper (US, CA) is greaseproof paper (Ireland/ UK, NZ) and baking paper (AU)