Yes, there are dozens of different solenoids and for sure more than one type of three terminal solenoid. Did you do the test I described? Here is another to determine the wrong type for your tractor. Across from one battery post to the other, touch solenoid small terminal and solenoid case (no big terminal involvement). Pull-in or not?
done the above test, yes it pulls in.
found the one came off tractor, the small terminal is to the right of solenoid and labeled "I"
The new one is to the left and labeled "s"