Uncirculated
A coin grade, a description of the condition of a coin. It can be taken literally as meaning a coin which has not been in circulation, and is therefore in mint condition. Because coins are mass produced, however, this does not necessarily mean absolutely perfect, and an uncirculated coin can be expected to have a few minor scuffs and marks.

Brilliant
Again this word means that it says, that the coin in bright and shiny with its original mint lustre. It is possible for coins which have not been circulated to have lost this lustre through less than perfect storage or handling. Most metal will tone or tarnish over a period of time, often due to atmospheric chemicals, although moisture undoubtedly speeds this process.

Brilliant Uncirculated
Means that the coin described is in mint, (although not necessarily perfect) condition with its original mint lustre.

The Royal Mint
We believe the British Royal Mint distorted the English language when it started issuing "B.U. (Brilliant Uncirculated)" gold £5 (quintuple sovereign) coins in 1984, but this potential confusion did not come to light until 2000 when it issued not only a B.U. £5, but also a "bullion" version.
These "Brilliant Uncirculated" gold five pound (quintuple sovereign) coins were struck to a superior but non-proof finish, and were issued in limited editions in boxes and with certificates, at a price over double their intrinsic gold content. When later in 2000 it then issued a "bullion" version of the same coin at only about 20% over gold, the error created some six years previously became exposed. This coin was brilliant (bright, shiny, and lustrous) and was also uncirculated (it had not been in circulation), although it was struck to a slightly lower production standard than the so-called "B.U." (Brilliant Uncirculated) version. When we expressed the opinion that people who had already bought the "B.U." version at £525 would be disappointed to find a brilliant uncirculated "bullion" version being issued at £325, a Mint official informed us that they were two different things, and that our criticism was quite incorrect. Perhaps the Mint should have added some extra description to its "Brilliant Uncirculated" products such as superior finish, specimen grade, monnaie-de-luxe, F.D.C., to differentiate these products clearly from those struck to a circulation grade of finish.
It remains our firm opinion that the Royal Mint has created confusion in its careless use of the term B.U. or Brilliant Uncirculated.

See also:-
Proof Versus Uncirculated
Bullion