Parchment vs baking paper
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.