You've already been introduced to the concept of "faction," but there's more going on, diplomatically, than just joining or avoiding the major alliances.
The factions do exert influence with their diplomatic points to draw countries toward them, ideologically. And often countries from two factions will get into a "bidding war" — each trying to influence a strategically located country in a sort of "tug-of-war" (so to speak).
But there are many other diplomatic options countries have to deal with each other. They may sign independent alliances, to protect from factions or other aggressive neighbors. They can agree to allow troops to move across their territory, send expeditionary forces, even permit a country to buy things on credit (i.e. war debt).
Independent from a country's alignment between factions (which is tracked on the triangular chart shown at the bottom of this screen), each country also has relationship levels between themselves. That, plus the "threat" certain countries acquire by doing aggressive things, helps determine how likely countries are to be friendly with each other, or declare war.
Countries begin with a neutrality level — their peoples' willingness to go to war, for any reason — and governments may have to take measures to reduce their neutrality in order to properly defend themselves against approaching war. When a country's neutrality is low enough, and another country's threat is high enough, they may end up at war with each other.
In order to fuel any economy — especially high-tempo wartime production — countries need resources (coal, steel, rubber, oil, etc.), and so there's an active "world market" between countries where they trade these items for money.
But any overseas trade must be carried across the ocean, and those convoy ships are vulnerable to being sunk by the purchasing country's enemies!