Something I wrote elsewhere, my understanding of what the different types of income represent:
• Tax Income is traditional income from land, such as feudal lords paying money in lieu of their traditional levies (as occurs increasingly in CK as the timeline progresses). It is closely linked to the fertility and productivity of the local area, and also to population (which thankfully is no longer tracked directly, as while it might have been flavoursome, it caused problems for modding and was extremely difficult to accurately research). At the beginning of the game, it is the most important source of income for almost everyone, but while it does increase, it is fairly static over the course of the game, and should be overtaken (gradually, then dramatically) by Production and Trade income.
• The Trade Good a province produces represents its primary export. Most provinces also have substantial agricultural production — that's represented in the Base Tax, above. A province will only be a Grain (or other food good) province if it was a very notable grain exporter or, more likely, if it didn't export anything else of note. Areas like Lombardy and the Low Countries, for instance, certainly had fertile agriculture, but they also had large local urban populations consuming that surplus and producing the manufactured goods we see as their province trade good (ie, Cloth).
• Production Income derives from the taxes on the sale of whatever your provinces' trade good may be to whoever is distributing it via the trade network.
• Trade Income derives from taxes on the buying and selling of goods up and down the trade network. If you are collecting a large proportion of trade in a node, it doesn't necessarily mean that those goods aren't travelling any further, it just means that your merchants have a strong controlling interest in the trade from that point on.
Over time, reflecting historical developments, Production and Trade should catch up with Tax Income and overtake it (please note that I am not at all sure that this happens to a satisfactory extent in vanilla. This is more of a design document for my mod). For highly developed countries with lots of trade interests, first, but eventually for everyone who is not very backward and shut out of world trade. By the end of the game, for the largest and most advanced powers, tax income should be an almost forgotten footnote in the budget, while control of trade and production of the most valuable trade goods is all.
If we look at EU's prequel and sequel games, we can see where we are going from and to:
• In Crusader Kings, there is no income from trade or taxation of exports, only local land tax. (Unless you are doing the Republic thing, which is a precursor of the longer distance trade that everyone starts to get involved in as the EU period begins.)
• In Victoria, there is no such thing as base tax from a province — all income derives from the production of goods and their conversion through artisans and then industry into increasingly valuable and technologically advanced end products.
The job of the EU economic system is to bridge the gap between those two. Successful countries will go from a local economy based on traditional land taxation to a global economy based on the export and carriage of the most valuable goods.
At the start of the game, when you want to know how valuable a province is, you check its base tax, while also noting any trade power bonuses, then lastly noticing its trade good.
By the end of the game, the order should be reversed: the trade good is by far the most important factor, followed by any strategic trade advantage (but that can always be obtained by buildings or more ships instead) and the base tax as an afterthought.
Edit: Oh, and Tariffs.
Tariffs are an unwanted overcomplication of the system now. The point of the new Tariff category in EUIII was that it forced you to build a large navy to get the full value from your colonies. (Navies weren't very important then, so people often skimped on this.)
You do still need one light ship or heavy ship for each overseas province you own to get the full Tariff value, but everybody builds lots of light ships anyway because they are worth Trade Power now. And you also probably want enough Heavy Ships that you aren't going to get blockaded in every war you get into.
So Tariffs are a historical vestige we're left with from EUIII. And their modifiers probably are not WAD.