Deere 650 is the same size category and age but I don't think they are twins.
TractorData specs:
Yanmar /
Deere
Manual transmission vs Powershift, 2 cyl vs 3 cyl, 2 more horsepower on the Yanmar.
2 gallon fuel tank difference. (Deere must have a larger cowl, there's no space for a 50% larger fuel tank on YM186).
Looking at
pictures it's obvious they came out of the same factory but I don't see the adjustable width rear axle or the same air cleaner on the Deeres.
I doubt there is much that would interchange beyond parts that are shared among many models - alternator etc.
As for YM186D / YM1501D - these are approximately the same tractor with different options for the US market. Internal pto overrun 'clutch' (ratchet), throttle is pull to shut off per US standards, ROPS, hydraulic filter, different air cleaner and tire sizes. I've read that the front axle assemblies are different.
Now if I could only find a YM186D as clean as yours! :)