The difference in these two logical fallacies is that DF is looking to make an option false while FD is trying make an option true.

I’ve moved the question to Psychology from English Grammar because this is a psychology/logic question and not a literary device one.

Below is a link to a website that lists out 26 logical missteps, with examples:

http://kspope.com/fallacies/fallacies.php

Ok – now to the question! The difference between a disjunctive fallacy and a false dilemma.

Disjunctive fallacy

results from thinking that within a choice between two things, finding one thing true makes the other thing false (even though they might both be true). For instance, I can say:

I bought the new car either because I like the colour or because I like the styling. I like the colour. Therefore I don’t like the styling.

In logic format, it looks like this:

##X or Y##
##X##
##”therefore not ” Y##

In logic, for the statement ##X or Y## to be found as True, either X or Y needs to be found as True. They both can be True – and so this logical fallacy negates one option that shouldn’t be negated.

False dilemma

results from thinking that within an array of choices, two things are chosen (and one is usually extreme) to force the “logical acceptance” of the second choice. For instance, I could say:

The punishment for a thief should either be 10 years of hard labour or death. It shouldn’t be death. Therefore it should be 10 years of hard labour.

In logic format, it looks like this:

##X or Y##
##”not ” X##
##”therefore ” Y##

In logic, for the statement ##X or Y## to be found as True, either X or Y needs to be found as True. If however we throw in a false choice (##X##), the remaining choice is forced to be seen as True.