Effectively, SPDIF (consumer format, unbalanced, normally characterised by the RCA co-axial connectors) is digitally simpler, whose basic information id unit utilises 4 bytes, (each byte being 8-bit).
AES/EBU (professional format, balanced, normally characterised by the XLR-type connectors) is digitally more complex, the basic information id unit being a differently structured 6 byte format (again each byte has 8 bit).
The differences in impedance are not critical, but the fact the AES/EBU is both digitally more complicated and generally of a higher operating voltage means that AES/EBU signals will not be recognised by SPDIF (consumer) equipment.
It is however possible, although not guaranteed, that an SPDIF signal may be recognised by AES/EBU (professional) equipment. You can always test this on your own equipment by constructing an adapter cable (RCA - XLR). Because of the lower operating voltage of the SPDIF signal, this will not distort the signal or damage your equipment. (good reason for not trying it the other way around!)
If you find that you do have compatibility problems due to the different digital formats, then you will need a converter. Naturally there are converters from other companies, but please feel free to compare the price / performance ratios of the units on offer before making your final decision.