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Provincal is a bonus to the base trade power generated by provinces you own.
Domestic is a bonus to trade power in trade nodes where you control physical territory and further boosts provincal trade power in those nodes.
Foreign refers to any trade node you have power in but have no territory, such as nodes where you're pushing trade through and using ships to generate power or nodes in which you are being transferred trade power but hold no territory yourself.
Mercantilism is yet another bonus to provincal trade power on top of Provincal and Domestic (+2% bonus per 1 point of mercantilism).
Caravan power is a bonus to trade power when steering trade through in-land nodes based on development, to compensate for the lack of light ships to boost trade.
Trade efficieny boosts the income gathered from trade but doesn't actually affect trade-power itself.
And trade steering affects how much force you can exert when pushing trade through contested nodes, and generally just means more trade goes where you want then would otherwise.
Wouldnt Global and provincial trade power be the same?
No.
Trade Power is generated by several sources: Provinces, a Merchant present, Light Ships, ...
Global Trade Power increases all of those whereas Provincial Trade Power only increase Trade Power from provinces.
Domestic trade power applies to nodes where you either:
a) have your capital/main trading port (depending on DLC)
b) are the dominant trade power
Those areas are immune to the trade power penalty for over-extension and get the domestic bonus. Areas that are not domestic are considered "overseas" for trade power calculations/bonuses.
Provincial trade power only applies to trade power generated by provinces, it does not apply to merchants or light ships.
Global, as previously mentioned, applies to all sources of trade power.