According to the American Heritage® Dictionary of the English Language, Fourth Edition. Copyright © 2003 (http://www.thefreedictionary.com) both terms denote the act of transporting something from one location to another (transportation, conveyance), yet "transferral" does not have the following meanings:

a) (figurative) the act of transfering something from one form/state to another ("the transfer of the music from record to tape")

b) (figurative) the application of a skill learned in one situation to a different situation or the link of a psychological response learned to one stimulus to a similar stimulus

c) a person or object ("the best student was a transfer from LSU", a ticket that allows a passenger to change conveyances)

However, I have my doubts as to whether this distinction is strictly adhered to in everyday language. I have come across "if you seek a tranferral of criminal proceedings", which is not covered by the meanings listed by the AHD for "tranferral".

Let me take advantage of the whole bunch of natives being around for asking you if you use both terms indiscriminately