Just like how your devices have multiple CPU cores, a super computer is just taking that to the extreme.
The same as is true for CPU vs GPU, where the CPU is designed as one buff processor to do big multi-role calculations, where the GPU is 100s or 1000s of very small processors designed to do only a few types of calculations. A way to think about it, is using division/multiplication, you can do both in more complex ways, with certain concepts like long division, or you can just keep adding/subtracting until you get the number you want. Both will get you to the same point, but one requires more initial brainpower, while the other requires a lot less split over a longer time.
You can technically do anything a supercomputer is doing, on a normal PC/Laptop/Phone (crypto is one example), but the reason a supercomputer exists instead, is primarily for it’s ability to communicate between it’s separate compute nodes (think cores, in a PC), at an acceptably high level, for any calculations relying on those calculations to be done, almost at the same time.
For situations where you don’t need the calculations to be done within a short timespan of each other (think the opposite of the weather node example u/sighthoundman used), it’s often more efficient to use Cloud computing. This is the same concept as a super computer, but the connection being limited to the internet, means it’s slower (latency), or slower (raw throughput), less secure, or less reliable (more prone to errors). Some of these are still done on effectively super computer type hardware, but split as more of a timeshare, and/or can be distributed to places where energy demands make it more economically efficient.
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