It is clear that Hobson's choice and Morton's fork (if it is accurately defined) are often confused with each other--including in the example used to illustrate the former. My mother (who was from England) taught me the meaning of Hobson's choice when I was young with the following example: "Would you rather have your head chopped off of your body or your body chopped off of your head?" (allegedly given to an unfortunate victim during England's Catholic-Protestant conflict.

The description of Morton's fork does not make it sound like a choice at all, but rather like an argument or rationalization for making all cases lead to the same desired outcome (eg, all people must pay taxes regardless of their financial status).