There seems to be two different versions of this series; one with 13 episodes, and one with 20.  Can someone explain the difference, please?  I've tried every Google keyword search I can think of, but haven't been able to find any info about this...

TIA!  :)

I tried Googling too and failed also. I did notice on the websites those with 13 episodes the parts are generally about an hour long whilst the 20 episode parts are 45 minutes though. I can't see any difference other than that to be honest. I could be wrong, as I've never completed the series, but I think the 13 episode is just a shortened down version of the 20 episode one. I'm guessing it was aired differently for a time slot for another TV station...or something like that? 

Might be best to wait for more replies though as I can't compare them properly because I haven't watched it fully.
I'm back because I was talking to someone who's watched this about it and apparently, from what they could conclude at least, the 20 episode version was aired in Japan and was cut down into smaller 45 minutes episodes to the Japanese standard for their television schedules. The 13 episodes (1 hour + ones) were aired in Taiwan who like the longer episodes for their dramas. 

So technically, other than the time length, there is no difference.
@zalcu - Thank you so much for your help!  I've been waiting to download this series because I thought there might be some major differences (story edits/cuts, etc.), but I'm glad to hear that's not the case!  Hmmm... I guess I'll go for the 13 episode version then.  I prefer longer episodes.  :D  Again, thank you!