Seconded to using the batteries. They go, and go, and go.
The output of the adapter is what matters. The input is different because your mains are different.
If you look closely at the adapter you'll also see a diagram that looks something like a C with a dot, indicating the polarity of the tip and ring of the plug. As long as they are the same on your two adapters, and it's putting out the same DC current, you're fine. And they should be, since both the MD and the PCM-M10 run on the same two AA batteries.