When comparing grade of coin with banknotes the first thing one need to
keep in mind that unc in coin mean simple uncirculated however since
there are many condition for uncirculated coin there are 11 grade
MS60-MS70.

When it come to banknotes unc does not mean uncirculated but actually
perfect condition and this is why there is technically only one unc
grade.

The term for gem choice etc when come to unc should only be used to
tell the perfection position so for example if the note was printed off
center than it is "less than perfect" and so it might be "just"
unc or choice unc while gem unc mean perfect position.

By the way one more nice to observe is that coin which are off center
have more value however in banknotes if it is off center it have less
value.
Of course this is only up to a point where the off is "so much"
off that it become error.

Ain't life great.

Have fun.