Effectively nothing. The two desktop torrent clients, uTorrent and BitTorrent used to be developed by two separate groups. Late 2006, µTorrent was purchased by BitTorrent Inc. Since then, they started shipping BitTorrent as a re-branded uTorrent, but also kept uTorrent around. Wikipedia
Because of this, they maintain one program, but have two versions separated only by name, and it seems as though they carried this over to their Android apps as well.
Agree with the user53233 that both were own by the same community but still feel that Bittorent is slightly better than utorrent. Following are the reason of my claim:
- In my 10mbps connection, BitTorrent performs better than Utorrent.
- when I checked both on MAC, Bittorent also feel slightly better than Utorrent. Here is a guide which can also second my opinion. https://www.vpnranks.com/utorrent-or-bittorrent/