most likely what happened is what TryNinja said, you have a clipboard malware
~snip~
I don't think OP is a victim of clipping board malware.
OP wrote that he is sure that the address he sent the coins to is the same as shown by binance:
..the address i copied was definitely the address that "binance" showed.
So, if OP checked the address before sending and he copied the right address, i only see 2 options at the moment:
1) Phishing site
2) Malicious wallet installed
1) is self-explanatory
2) OP, what wallet were you using? Are you sure your wallet is a trusted one? Did you check the signature to verify its not a fake (malicious) wallet?