Can two different firmware files have same md5 sum?

Can two different binary files have the same md5 sum? One binary firmware file have different version number and marked as revised, small bug fixed. But both files have same md5 sum, I would assume that revised file can't have the same md5 sum - can this be a mistake?

Of course. MD5's collision vulnerability is well known (see Crypto.SE, Wikipedia). Though it is still a low-probability event, it can be done. However, in your case, I'd suspect a mistake in copying the files.

What the existing answers fail to point out is why a collision is deemed to be vanishingly unlikely in this case.

MD5, like any hashing algorithm, was deliberately designed so that a collision won't happen if you just change a handful of characters. You have to change most if not all of them in order to cycle back around to the same hash. That's because the whole point of a hash is to detect single-bit (or few-bit) errors; in this problem domain, you want the smaller changes to definitely trigger a hash change. Flawed though we now know MD5 to be, that property holds to this day.

So, unless the new version of firmware is completely different, and unless you just witnessed a once-in-a-million phenomenon, the odds are huge that you simply received the old version again. Congratulations, because this is the hash-check process working precisely as intended. :)