Not much really. They're both used to download torrents from host trackers. They also have different user interfaces, so up to you on which do you prefer. Utorrent is has a more basic and user friendly interface, thus more popular.
utorrent is a bittorrent client. utorrent is much smaller (in size and footprint) then bit torrent's official client, and so it runs faster. The GUI is also quite different and there are more options. utorrent is probably the best bittorrent client out there
Bit-torrent is more steering towards the "Buy premium or we spam you with ads". Utorrent is less, but since bit-torrent and u-torrent are based on the same code, they may seem quite similar(in looks anyways). BIt-torrent's UI tends to run slower and use more resources because of the ads, and background processes.