They are different: a false dichotomy is a false presentation of two choices as being the only possible choices and necessarily mutually exclusive of each other. A false equivalency is falsely maintaining that two unequal things are the same.

I could have used either in this case. His statement that disliking codemonkeyz is the same as disliking q could be simply referred to as a false equivalency. However, I framed it as a false dichotomy in this case, because he is making the point that I cannot possibly have one opinion of cmz without having the same opinion of q.

From wikipedia:

“A false dilemma, also referred to as false dichotomy, is an informal fallacy based on a premise that erroneously limits what options are available. The source of the fallacy lies not in an invalid form of inference but in a false premise. This premise has the form of a disjunctive claim: it asserts that one among a number of alternatives must be true. This disjunction is problematic because it oversimplifies the choice by excluding viable alternatives. For example, a false dilemma is committed when it is claimed that "Stacey spoke out against capitalism, therefore she must be a communist". One of the options excluded is that Stacey may be neither communist nor capitalist. False dilemmas often have the form of treating two contraries, which may both be false, as contradictories, of which one is necessarily true. Various inferential schemes are associated with false dilemmas, for example, the constructive dilemma, the destructive dilemma or the disjunctive syllogism.”

“False equivalence is a logical fallacy in which an equivalence is drawn between two subjects based on flawed or false reasoning. This fallacy is categorized as a fallacy of inconsistency. Colloquially, a false equivalence is often called "comparing apples and oranges."