Strangely enough, there are reasonable grounds for calling them both real. Real, in the historical sense, your humble interlocutor shall explain.
While most of what constitutes the genre of steampunk fiction is mainly romantic and glamourized version of a steam-powered nineteenth century reconstructed as fantastic adventure and often in the form of various kinds of retrofuturism, if one looks back at what the transformation of their era was like for the people who lived through, then they were in a world that seem like a steampunk world.
The Industrial Revolution unleashed not only new technologies (steam-engines, sewerage, clean water, machine-guns, the chemical industries, and eventually the internal combustion engine), new forms of transportation (the railways, steamships new roadworks, agricultural tractors, and, latterly the bicycle), and new forms of social organization (Parliamentary democracy and the Education Act which unleashed mass literacy), and the new scientific worldview (evolution, chemistry, physics with electromagnetism and electricity, and geology).
The creation of a new technologically dominated world in the nineteenth century was everything steampunk could deliver. Not as mere fiction, but as actual quotidian reality.
For reference you should refer to LTC Rolt's fascinating history Victorian Engineering (1970). Rolt is a good place to start if you want to immerse yourself in the reality of industrial history and find out the real steampunk was like.
Now looking into a grim-besmirched crystal ball what visions of the future does this bring? OK. Consider a straight forward extrapolation of current trends. Robotics promises to drive the entire working class, followed by the soon to be redundant middle classes, into a permanent underclass. The super-rich continue to become super-richer while the rest of us only grow poorer. Total surveillance via ubiquitous smart-phone technology, closed-circuit TV, and boosted with image-processing software for instant identification Politics reduced to show business, and riffing off fear, anger and toxic hatred. The rise of the alt-right, neo-nazis, and other political tinfoil hat brigades becoming effectively mainstream politics. The supplanting of citizenry with consumerdom. Business, financial and commercial institutions reducing governments to their marionettes.
Add machine intelligence, virtual reality, permanent cyber warfare and the infiltration of control systems connected to the internet, and what have you got? This could be our future. A future that is pure, authentic cyberpunk. 1
For reference: George Dyson's fascinating history of the development of the first modern computer Turing's Cathedral: The Origins of the Digital Universe (2012). Effectively we're half way there to a highly cybernatically dominated and controlled world. A bit more integration and increased interconnectivity and we'll be there.
In conclusion, "(h)istorically speaking, what point of departure do I need to make either punk a reality?" For steampunk, go back to the historical reality of the Industrial Revolution. Your main problem will be to communicate the fact that the real historical industrial past was in and of itself a steampunk world. While for cyberpunk it's only a matter of looking ahead and seeing what's already coming. If current trends stay on course we're heading for a world that will pure cyberpunk.
So what points of departure are needed to make either punk real? None, just stick with historical and probable-future reality.
1 Unless, of course, the future pulls one of its almost inevitable switcheroos and swerves into a completely different direction. The future's like that.