Both Shiro and Satsuma are Asian (or Japanese) plums and can be pollinated by any other Asian plum....choice #2 :-)

And to answer your primary question, you really need to see the fruit to determine variety. They all look pretty much identical otherwise.

Apricots can also pollinate Asian plum.

So to can Asian flowering (ornamental) plum.

You should always keep tags on your fruit trees so you (and future owners) know what they are.

Now that you lost the tag and can't remember which one you have, the most sensible option might be to buy some third variety of Asian plum that you know is different from what you have. Either that or buy two more trees of each variety.

Shiro and Satsuma are entirely different varieties and easy to identify. The Shiro is a small yellow fruit that typically sets prolifically. The Satsuma is a greenish red skinned plum with very deep red flesh. Shiro is self fruitful and does not require a pollinator, but could be a good pollinator for the Satsuma.

In answer to your original question i would recommend planting another self fruitful variety that would pollinate the Satsuma if in fact that is the one that remains. That way if it is the Shiro that remains at least the new planting will not need any special variety to get it to set fruit. I would recommend either the Santa Rosa plum or the Beauty Plum.

Thank you!