The two most obvious differences on 1804 Half Cents relate to the 4 of the date. On some coins the horizontal crossbar of the 4 ends with a vertical crosslet; on others the 4 has no crosslet. The Crosslet 4 is slightly lesscommon than the Plain 4.
The Plain 4 obverse is combined with two different reverse types: Stems at the base of the wreath and No Stems at the base of the wreath.
Only one die variety (Cohen 13) qualifies as the Plain 4, No Stems variety.
Uncirculated examples of the 1804 Plain 4, No Stems Half Cent are scarce, but are the most "common" of any of the 1804 Half Cent varieties. Brown Mint State examples are the easiest to find. Red-Brown examples are much tougher and full Red examples are exceedingly rare.