Boeing B767-200/-300 are developed in 1980's to respond to the fall of trans-Atlantic air traffic. They are the smallest & narrowest widebody in the world, and were the only 200 seaters having over 7000km range before A310-300 & A300-600.
Because of its long range, 3-hour ETOPS compliance, widebody comfort, and better economy due to 2-engined design compared to the trijets, it is very popular everywhere. It enabled the operation of more point-to-point routes, and enabled retirement of old, fuel inefficiet 707, DC-8 & 727 serving Hawaiian routes.
Boeing then developed 767-200ER & 767-300ER of over 10000km range in early 1990's, the only 200-seaters having over 10000km range. This makes B767 even more popular, and much lowered the sales of competitor Airbus A300/A310 of 1970's design.
Boeing finally developed B767-400ER 250 seater of 12000km range to compete with A330 in late 1990's. But its sales is poor because of lower seating capacity & poor economy compared to A330-200.
Boeing decided to drop down MD-11 300-seater since 2001, but did not have any plans to develop jets of size between B767-400ER & B777-200. This makes Airbus A330-300, A340-300 the only 300-seaters since then. This and Boeing's decision of not producing smaller quadjets makes many airlines, especially the Southern Hemisphere airlines, switched to Airbus A330/A340 due to more commonality for lower cost and ETOPS-free design of A340 for shorter & more reliable trip.
It is so strange that Boeing B767-300 is the only variant having Rolls Royce RB211-524 engine option, while GE CF6-80 & PW4000 engine options are available for all variants. This makes some airlines prefer Rolls Royce engines, like Air Canada, British Airways & American Airlines, have to use non-Rolls Royce engines for all B767, thus greatly increasing maintenance cost. This also makes some airlines that strongly supports Rolls Royce engines, like Cathay Pacific, Thai Airways, Singapore Airlines, Air India, etc, refused to introduce any B767 models. What a serious mistake for Boeing & Rolls Royce!