damaged

I have a betta who used to live in a 0.5 gallon bowl with one little plastic plant. He was happy as could be! I have since moved him to a 5gallon tank with two more plastic plants. There is also water flow into this tank, creating a current. Now his fins are all torn up and ragged looking, and...

Okay, just found this little guy at Petco today, and thought he was so adorable, so I had to have him. He was labeled a Halfmoon, but he looks like an Elephant Ear to me...what are your thoughts? Also, do you think he has fin rot? or are his fins just damaged. He has torn/bad fins on his tail...