I believe the 2.0 engine your refering to may be the mazda 2.0. Prior to the ranger there were mazda b2000s, mazda b2200's and Ford couriers. The b2000 and b2200 had the same bodies as the couriers ( 2 body styels, they changed in 76/77. The mazdas and some couriers got the 2.0 engines, hints the name b2000, while some couriers got the 2.3, and the 2200 got disels. there were mazda b1800 and b1600 but those arent important right now. In 1982 ford pulled the plug on the project and started their own mini truck the ranger for 1983, while mazda continued the the trucks until 1984, then they redesigned them for 1986. But enough with the history lesson here.
If your engine seems to have a wide short vavle cover, then it is probably a mazda engine. As far an interchangibilty goes, the engines are of 2 diffrent designs so dont count on swapping stuff here. Example the 2.3 is and external belt driven ohc where as the 2.0 were chain driven. They used diffrent trannies, mazda had there series II i believe where as rangers got the borg warner.