What types of capacitors should be used when?

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I searched back about a year and couldn't really find it.

I'm asking about basics - how does a designer know that an electrolytic is called for rather than say a film type of the same value?

I've seen lots of schematics so I'm getting a feel for what is typically used, but I don't know why. I'm not asking about what sounds better, brands, exotics like pio, etc. Just looking for some sound engineering grounds for the choices made.

Yes, the topic is a rather broad one, that could fill many forum pages.
To your specific question, it all comes down to function and cost. Electrolytics are leaky, don't age as well, and have relatively high ESR. But they do have large values in a relatively small package. If those characteristics fit the circuit, an electrolytic can be used. If those characteristics don't fit the circuit (e.g. you wouldn't want a leaky lossy cap in a finely tuned circuit) then a film cap is the appropriate choice.
Most electrolytics need a DC bias, in order to maintain the oxide layer, so may be inappropriate for places where this is not possible. Fortunately, most of the time you need a big capacitance there will be some DC.

It turns out when designing most circuits it is fairly obvious when an electrolytic is appropriate, based on required value and available space (and cost). There is an overlap region where a small electrolytic or a big film cap could do the job - then it may be just a matter of personal choice.
What they said^^^

The designer determines what value cap he needs. The type of cap is then more a matter of filling that need practically. A 40uf 450v film cap would be immense, while an electrolytic of those specs would be the size of my small finger.

If you make a parts list of all your cap needs, you will probably mainly be using film caps, so go down the list and enter part numbers for all that you can find in film. You will find some values you just can't find in film, mostly the larger ones, so then find them as electrolytics. And somewhere where the two columns fade one to the other, you may find in both forms, so then look at the film in terms of size and cost, and make a choice. And on the small end, I just had a discussion about this a day or two ago with someone for his guitar amp. If you need something like a 250pf cap, you may not find it in film, and for that you would have to look at ceramic or silver mica or some other type.
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