One flybase gene number (FBgn), many Affymetrix Id's
I can answer this - I may not have time to dig though the file you are pointing to... but here's some explanation - lmk if you need more.  

The shorter names (123456_at) are the original names for the probe sets that Affymetrix gave.  The file you area asking about has been extended for FlyBase's purpose and I'm only dimly aware of its existence. It looks like Flybase has tried to rename the probe set to a minimal gene list and create less ambiguous mappings.  I'm not familiar with it.  If I have time Ill try to look at it and put something here, but I'm fairly slammed this week. 

In general you should know, there is a many to many relationship between probe sets from arrays and genes.  

There are a few reasons for this.  The most common reasons: 

More than one probe set per gene
1) More than one start sequence per gene. The IVT arrays such as you are looking at read only the 3' end of the gene.  If there are  more than one such terminii, you will have more than one probe set. 
2) Duplicate genes.  If the 3' end of the gene has been duplicated recently, then a probe set may read more than one gene and not be able to distinguish them, so it will have both gene references in its annotation files. 
3) Duplicate probe sets. For older arrays, this did happen where the probes in two probe sets will be mostly or entirely the same. 
4) formerly separate genes are now joined into a single gene.  This is similar to (1) above, but with the added reason that two neighboring transcripts seen separately at the time of the array design are currently known to be part of the same transcript.  This is something we often don't think about, but the array may have been designed before your current gene of interest had a full length sequence.  

In several cases the transcription behavior of the two probe sets will be quite different and you can decide which one to take based on how it behaves experimentally.  for example one of the probe sets may never respond while another one may register large changes with biological sample conditions.  Sorry I can't be of more help here. There are too many possible scenarios to consider to write about cogently.  

More than one gene per probe set 
1) a single stretch of DNA, even on the same strand, may simply be associated with more than one gene and the probe set will read both of them. 
2) Even if they are not exactly the same, some genes resemble each other in nucleotide sequence that is impossible to choose probes which do not read both of them.  

Since they have similar read length to a probe set, all this is also true to some extent for short read NGS sequencers in RNASeq data. 

As you can hopefully see, ambiguity is something you have to expect to some extent when deciding to work with a biological system.  In many cases (~ 80%) you will have a single gene read per probe set, but with those odds you'll be looking at the genome browser for a half dozen of your favorite experimental results.