BU vs. MS - should be simple, but I'm confused: Please help!

Where does BU fit in on the scale? Better than MS60? MS63? Not as good? Why do some dealers at shows put BU on the 2x2 and on other coins will put MS whatever. Please fill me in on this mystery.
tom
tom
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In the old days there was just Good, Fine and Uncirculated.
But because some uncirculated coins where better than others, terms like Brilliant Uncirculated, Choice BU, and GEM BU were invented.
In 1948 the “Sheldon Scale” assigned grades from 1 through 70 to coins. His theory was that an MS-70 would be worth seventy times as much as coins grading just 1. Although many collectors agreed on the scale, they could not agree on standards. And the Sheldon Scale Grade was still a matter of subjective opinion.
So think of uncirculated as MS-60, BU as MS62, Choice BU as MS63 and GEM BU MS65+
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want to grade it to the number for better realization of value.
Its the BU range thats so tricky.
The dealer will sell you a coin as BU,two days later will buy it back as an 58.
58-63,they look really similar sometimes.
time it really meant just "no question unc". It was a coin with full original
luster which was unimpaired. It could be any grade from MS-60 to MS-70.
As more terms came into use to differentiate these grades it's meaning e-
volved. Today it seems to have taken on two meanings depending on who is
using it: It can be nice attractive unc (MS-62/63) or it can mean nice fully
lustrous coin which isn't good enough for any of the superlatives (MS-60/61).
Most agree it still has the "no question unc" meaning.
K S
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