Why it decides the price
A price quoted FOB and a price quoted CIF are not comparable numbers. The difference is freight and insurance, and on a long route that is a material share of the delivered cost. A buyer comparing a CIF offer against an FOB offer without adding freight will pick the wrong one.
The four you will meet most
FOB — Free On Board
The seller delivers the cargo onto the vessel at the named loading port. Cost and risk pass to the buyer once it is on board. The buyer arranges and pays for the vessel, the freight and the insurance. Suits a buyer with their own shipping arrangements or better freight rates than the seller.
CIF — Cost, Insurance and Freight
The seller arranges the vessel and pays freight and insurance to the named destination. Risk still passes at the loading port, which surprises people: the seller pays for the voyage but the buyer bears the risk during it. The insurance the seller buys is the buyer's protection.
CFR — Cost and Freight
As CIF, but the seller does not provide insurance. The buyer must arrange their own cover, and a buyer who forgets is uninsured for the whole voyage.
Ex-Tank and TTT/TTO
Delivery inside a terminal, either into the buyer's tank or onto their vessel, without a sea voyage. Common for smaller volumes and for parcels changing hands within a hub such as Fujairah, Rotterdam or Singapore.