Numbers that are actually letters

Pyth, 43 - 40 = 3 bytes

?&[email protected]"Mix"%"Only %sers"?K"lett""numb

Test suite

This achieves the bonus. Only numbers and Only letters fortunately only differ by 4 letters. printf-style formatting is used with %.

The selection system is done by both taking the intersection of the hex with G, the alphabet, and subtracting out G. If neither ends up falsy, it's a mix, while if the intersection is falsy, it's numbers, and if the subtraction is falsy, it's letters.

Pyth, 6 bytes

!-.HQG

  .HQ   # Converts the input to hexadecimal
 -   G  # Deletes all letters
!       # If empty, output True, else False

Test it here

Jelly, 6 bytes

b16>9P

Try it online!

How it works

b16>9P  Input: z

b16     Convert the input to base 16.
   >9   Compare each resulting digit with 9; return 1 iff greater.
     P  Take the product of the resulting Booleans.