I was thinking about getting some EOS recently, so its good you did this article. EOS has been storming lately, and I have been getting interested just because its Dan's brainchild. I can get it on Binance now as its listed, but the fact that you can get it as a token directly is a little confusing.
Is there any advantage of buying the tokens over the Binance EOS, or are they in fact the same thing?
They are in fact the same thing, but their price could be different. At an exchange, you buy them at a fixed rate. If you buy them through the official EOS token sale, the amount of tokens you receive is based on how much is invested in ETH for that current round. The difference usually isn't that much.
When you buy them via an exchange, you must make sure that you transfer the tokens either to MEW or Metamask. Do not leave them on the exchange, because you cannot register an exchange's ETH wallet for your EOS distribution you would receive after the 1ste of June.
Here's a page with detailed instructions:
https://eos.io/instructions