I found this online, but as a native speaker, I didn't even know this.
I don't think you really need to worry about distinguishing them.
In addition to the text below, "partially" sounds more formal.
Hope this helps :)
These words are almost interchangeable and I don't think there is a case where it would be wrong to use one and not the other.
There is, however, a pretty simple rule for common usage:
Use partly when the "in part" is part of a tangible whole, and partially when it's not.
For example, if we say "The door is partly open", then we can easily see that it's also "partly closed". In the phrase, "Her life was partly tedium", we easily infer that her life was partly excitement.
Partially is used when we can't say that the part we're specifying is part of some tangible whole.
"His explanation partially explained it." You wouldn't say "His explanation partly explained it, and partly didn't explain it", so you use partially.
However I should make clear that both are correct in all of those sentences. It's not wrong to say "His explanation partly explained it."
The only exception I can think of (I'm sure there are more) is "partly cloudy" or other weather-phrases just because those are common phrases burned into our minds.