Hi Mehdrad,
As the others have pointed out, the 2 sentences mean the same thing.
Out of context, the 2 sentences seem equally likely... but they really aren't. 'Would' is more likely to be used in writing or more formal spoken situations. 'Did' is more common in casual, everyday spoken conversation. Informal spoken conversation tends to be really quick and easy... people choose simple verbs, like 'did', and express shades of meaning in tone of voice and body language.
I hope this helps! :)