My atari 2600 has no sound, which is a common problem with an easy fix, just replace 2 capacitors. The original capacitors are 820pf polystyrene axial capacitors, and these are a bit tricky to find. Could I just replace these with any other kind of capacitor like an electrolytic or ceramic one? DO they do the exact same thing or are they different?
Polystyrene caps are no longer made. Their major disadvantage is the low melting point of the film, so they can't be machine soldered, only hand soldered.
Back in the bad old days, they were used when a high tolerance was required. If that was the reason these were polystyrene, then any plastic film capacitor of the tolerance would be suitable.
The main specification advantage of polystyrene is its low dielectric absorption, which only really shows up in professional instrumentation-type sample-and-hold applications. Where this is absolutely necessary, use polyphenylene sulphide (PPS) or PTFE dielectric film capacitors to replace it. Unfortunately, both these types are tricky to come by, and expensive.
Polypropylene film is very nearly as good as those, and much more available.
Polyester film is the standard film capacitor dielectric, widely available and cheap, and still very good performance. It's worth trying this type first, to see whether it does do the job. You can buy these in high tolerance values.
You won't find electrolytic caps that small. Don't use ceramic either.