I have not seen model number AV0039-51A - I suspect it is not available in the US or associated Citizen markets. Can you expand on where you have seen this?
The other model you mentioned, AV0031-59A, differs in 2 ways from the AV0039-51A.
1) The third-last and second-last characters relate to the bracelet - so we can tell these two watches have a different bracelet. (The "A" at the end just refers to the dial colour, black).
2) The "AV****" part relates to the watch movement and case. These numbers are CLOSE on the models you mention, so it's likely that the watches have the same movement - however I can't say for sure.
If I were to guess I'd say that these watches are near-identicay, but with some small regional differences (e.g. AV0039 could be the version sold in South America, Asia, continental Europe or some other market with slight case differences from the AV0031 version). But without a picture I can's say for sure.