Yes and no.
The BII ran from 84-90. IN the later years the 2.9L Cologne 60 degree V6 was bored out and turned into the 4.0L OHV (thank god). This was the new engine that would power the Aerostar, Ranger, and the New heavier Explorer.
Some early 4.0L's were found in late model Bronco II's (I have only seen one factory BII with a 4.0)
However some of the 89-90 BII's also had the exact same interior as the 91 Explorer (from front seats forward).
Also 89-90 BII's have been seen with a Dana 35 TTB front end (84+ BII's came with a Dana 28 TTB front end) still keeping the MAS 2.9L engine and 7.5" rear axle. I have seen a few of these.
The Explorer was the 4 door Bronco II. Ford addressed many of the BII shortcomings when they designed the Explorer. The 2.9L was borderline (albeit a strong engine!) when it came time to motivate a 3500# 4x4 BII. The new 4 door would weigh even more so they needed more low down torque.
The BII axles also were a little weak (especially with higher miles) and the ride was rather rough with the spring over rear leaf setup.
The Explorer was built with a stronger drivetrain, the VERY strong 31 spline 8.8 rear with a spring under ride.
I have also heard rumors that some late 90 BII's had Explorer badges on them, but for all I know this was a dealer ploy or a myth. but you never know, I have seen Ford do some weird stuff, with all their vehicles, its like they grab whatever was on the shelf....hehehehe
If you strip a early Explorer (91-94) and do the same to a BII (89-90 BII's had the same front clip as a 91 Ex) you will see minor differences, the 4 door Explorer is basically just a little longer from the front seat back. They put the gas tank on the drivers side frame rail in order to make room under the truck for the spare. The leaf springs were located further apart and under the rear 8.8 so the rear end would track better and ride much smoother. The BII has a tendency to get sideways on washboard if you allow the springs, shocks, and bushings to get worn (like a Jeep). The Explorer is really a hell of a truck if you ask me, they are a reliable capable workhorse...
So the BII has been called the early Ex many times. You know they really didnt change much from 1984 all the way to 1995 when the IFS replaced the TTB. They continued to build the D35 TTB in Rangers until 97 I believe.
The first Explorer sports and Mazda Navajo's are even more similar to the BII and pretty much all BII and Explorer parts are interchangeable without any real modifications (at least drivetrain wise). You may have to weld the spring pads on the top of the 8.8, do some driveshaft modifications, etc if you want to "upgrade a BII" or put a small body lift on the Ex if you want the BII gas tank, but other then that they are big brother/little brother.