I can’t explain the difference between those two.
Spiegarti is implying he is making this comment to a familiar, correct? If subject were to make this statement to himself it would become spiegare or spiegarsi? Just want to confirm because even the AI translation never makes it clear that the subject is speaking to someone when he makes the statement.
I read it as “I don’t know how to explain to you the difference …” What do you think?
I think you are right. A familiar single one, to be precise.
IMHO “…spiegarti/spiegarvi//spiegarle …” are all possible translations of “explain to you”.
I am not sure about “spiegarsi” in this sentence.
Maybe “…spiegarmi …” if somebody would be mumbling the sentence to himself?
Spiegarsi - “I don’t know how to explain to one…” it works I think but not too sure about spiegarmi 
I think “non so spiegare la differenza” is the best translation, without context.
“Non so spiegarsi”: doesn’t make sense to me.
“Tom non sa spiegarsi la differenza”: Tom is at a loss about the difference [?]
I like and go with your first example. What about the spiegarti part? Would be interested to hear more🖐