The difference between the burnished uncirculated silver eagle and the uncirculated bullion silver eagle is that the rarer burnished variety bears the "W" mint mark on the coin and was intended for collectors - while the bullion uncirculated coins do not have a "W" mint mark and were intended for bullion investment.
Rare variety to watch out for: In 2008 there was a major design change on the reverse of the coin. Most burnished silver eagles of 2008 (533757 minted) have the newer design. Although a smaller number of them (47000 minted) still had the older design on the reverse of the coin - used in 2007 and in earlier years. This variety is one of the rarest and most valuable silver eagle varieties.