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FIA and Bank of America are the same company. If you look at the bottom of your statements it will say FIA. Also if you request any rewards it may include that, too. If you go past due they (Bank of America) may use FIA or Card Services as their "internal" collections department, they are just another name for their company. Don't worry about it.

FIA and Bank of America is both are handle by the one company. So, you can easily transfer money and also change the cards of each bank with other. How to change it, That steps are given in this link -http://www.usignp.info/2013/04/fia-card-services-c...

You will probably have to go with Bank of America's terms. FIA manages Bank of America credit cards.