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Here are Perth Mint's definition of Proofs Bu's and Specimen coins,I've added a few coins to hopefully clarify things,the proofs are all on the left of the photos
 
 
Proof Coin
The very highest quality collectable coin produced by The Perth Mint.  Featuring a proof finish comprising a highly-polished table with frosted and/or coloured design elements.
Bullion Coin
A mass produced coin primarily aimed at precious metal investors. Finished with shiny design elements on a frosted table.

Specimen Coin
A collectable coin akin to a bullion coin with a frosted table, but also featuring one or more special numismatic treatments, including colour, gilding, antiquing, or the insertion of gems.
 
2oz lunar 2  snake  proof and BU
 

 
Same coins showing obverse
 

 
1oz Lunar 2 mouse proof and Bu
 

 
Same coins showing obverse
 

 
1/2 oz lunar 1 rabbit proof and Bu
 

 
Same coins showing obverse
 

 
RAM's interpretations of proof and Bu,s also known as UNC/uncirculated.
 
Proof
A carefully struck coin using special dies with either a mirror‑like or matt finish. These coins are especially struck and the term is not used to describe a well‑preserved circulating coin. Proof is a method of manufacture, not a condition or grade.
  Uncirculated (UNC)
Uncirculated coins are manufactured in much the same way as circulated coins except for the following:
More attention and time is given to the preparation of the die surface finish, The coins are struck with greater pressure than the circulating coins to improve the sharpness of the design. More care and attention is applied at each step in the coining process to minimise damage, consequently a much lower production rate of about 30,000 coins per press per day is achieved. Uncirculated coins are packaged individually into plastic sleeves, presentation folders or occasionally presentation cases.  
1oz 2000 proof and Bu from RAM
 

 
Same coins obverse
 

 
I hope this helps clarify things.

2011 Britannia masterpiece, 8oz or 250g

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