A false dilemma presents two options as if they were the only ones. 'Either we cut this program or the country goes bankrupt.' 'You're either with us or against us.' The trick is that the framing itself does the arguing — by the time you're picking a side, you've already accepted that these are the choices. The response isn't to pick better; it's to reject the frame and name the missing options.
A slippery slope claims one step inevitably leads to an extreme end state, without establishing the mechanism connecting them. 'If we allow this minor regulation, we'll end up with total state control.' Note that slippery slopes are only fallacious when the causal chain is asserted rather than demonstrated — some slopes are real and documented. The question to ask is always the same: what's the actual mechanism that makes step two follow from step one, and is there evidence it operates? If the answer is 'it just would,' you're looking at a fallacy wearing a prediction's clothes.
The false dilemma is powerful precisely because it hides its work in the setup rather than the conclusion. Logicians classify it among the informal fallacies — errors not of form but of content, where the argument's structure may be flawless while a premise quietly smuggles in something false. The premise 'there are only two options' is rarely stated outright, which is what makes it hard to attack: an audience given a binary choice tends to start evaluating which option is better, and in doing so has already granted the premise without noticing. Douglas Walton's work on informal logic makes the point that the correct response to a false dilemma is not to argue for one horn but to challenge the disjunction itself — to say 'those aren't the only choices' before engaging at all. The same structural analysis applies to slippery slopes, which Walton notes are not automatically fallacious: they become fallacious specifically when the argument asserts an inevitable progression without supplying the causal mechanism that would make each step follow.