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.