Are there words or concepts for ‘Real Chocolate,’ Obligatory Chocolate’ and ‘Reverse Chocolate’ for Valentine Day gift in English?

Solution 1:

In the US, the Valentine's chocolates are often given from the man to the woman, and there are no special designations of chocolate.

There are, however, designations when flowers are given. The type and color of flowers given on Valentine's and other days have meanings. Red roses are supposed to mean "I love you" and would be equivalent to your Hon Choco or Cyaku Choco (again, the roses are usually from the man to the woman). The meanings are often set by the flower companies, so they are as much an advertising gimmick as having any historical meaning.

On Mother's Day, at least in the past, a woman or girl would wear a white or pink carnation -- white if her mother was deceased, pink if her mother was still alive. That custom seems to be falling by the wayside.