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Does it work that way? I don't think so. Because you transfer your money to a wallet. But, perhaps you are correct.

Yes. I'm sure that this is all that is happening.
I just opened up my bittrex account and my poloniex account, and looked at how I would transfer between the two of them. And this is EXACTLY how to do it.
I would have to send Steem held at Bittrex to the Poloniex account on steemit, or vice-versa.
So there is no great mystery here.

Great. Good to know. Thanks

Exactly right.
People decided that they prefer one exchange over the other,
or they are trying to benefit from arbitrage -- when steem is higher on one exchange vs the other. So they send it back and forth.