While browsing the ECU files sites, I saw 3 different identifiers of a file:
ECU number (For example EDC15C2, IAW5AF)
HW (hardware) number (For example 0281012982, 5G0906259P)
SW (software) number (For example 1039S45097)

Could anyone tell me what is the difference between those identifiers? And what do they actually mean?
Could the same ECU have different HW/SW numbers?

But what does every one of them mean?

The identifiers you are asking con be broken down to

ECU number = The electronic control unit model
HW (hardware) number (For example 0281012982) is in your example the bosch hardware number
P/N (oem) number (For example 5G0906259P) is the oem part number for replacement
SW (software) number (For example 1039S45097) is in your example the bosch software number

Beware that using only these identifiers does not give you a 100% match with your BIN file! There are other numbers & alfanumeric texts in the file that are more specific... for example BMW EDC16/17 you can search for the alfanumeric text that starts with O_ (length varies sometimes 8 digita sometimes 21) and also for the numerical 11 digit number that starts with 37

and the list continues every manufacturer has it's own way of identifing the ecu.