What is meant by "same difference"?

Unless you are comparing two different sets of items to then have a couple of differences and the differences are the same, I do not get it.

This would be analogous to: 12-9=3, 7-4=3. Here we have the same difference.

The problem is, I really don't think the average human is comparing two differences when using the term in question.

Solution 1:

Same difference is an idiomatic oxymoron [Oxford Dictionary Online]. It effectively means

Whether these two choices are the same or different is immaterial to me.

SUPPLEMENT

The Urban Dictionary defines it as follows:

Another way of saying "whatever". It is often confused with "same thing", but you're really saying "OK, I admit that they're not the same thing, but they're not different enough for me to really care about it."

The Cambridge Idioms Dictionary defines it as

the difference between two things is not important

Solution 2:

The expression is used to indicate that objections or differences between alternatives are of no or little importance or consequence.

Compare it to the use of "Whatever" to dismiss an objection.

Solution 3:

People already defined it as meaning there is little or no difference between things being compared. I can't comment, so I am answering with my input.

A good example (meaning about the same thing) is "six of one, half-dozen of the other." (A dozen being 12)

Another is "To-MAY-to, to-MAH-to".

All of these are informal, but imply that they are the same thing. It is sort of a way to dismiss a straw-man argument, or more likely someone nitpicking details in a story.

Me: "My cousin Joe is a dumb hillbilly. He crashed his truck into a fencepost while drinking Bud Light!"

Insufferable bore: "Actually, he's a redneck; hillbillies come from the Appalachians. And he was drinking Keystone Ice."

Me: "Same difference."

This exchange implies that the details don't matter; his cousin is a 'low-class' drunk, regardless of the particulars.