What this coin looks like (obverse, reverse, mint mark location, special features, etc.): There were a few major varieties of the 1837 Coronet Head Large Cent (Penny). Two varieties deal with the design of the portrait of liberty on the obverse of the coin. One variety is the "Head of 1838" which features the newer design of liberty. The most notable feature is that the cords around the hair are beaded. The other variety is the "Head of 1837" which features plain cords in the hair. The differences are depicted above in the example comparison image.
There were also two varieties within the "Head of 1837" variety. Both of them have "plain cords" in the liberty's hair on the obverse of the coin but the lettering on the back of the coin is different. One variety had medium sized letters and the other had smaller sized letters. The differences between the medium letters vs small letters is depicted below in the example comparison image of the coins. Note the size of the lettering and the spacing between the letters as well as the alignment of the letters relative to the wreath: