Render cache, EXR files?
The render cache ist the Part of the memory where the render result (the rendered image) is stored.
What is EXR.
Yeah, I’ve enabled the button and rendered some stills and some animations but I can’t find where it is placing the EXR files. My PNG comes out into the file I want it in and the EXR is nowhere to be found.
the cache will be stored in an EXR format for further composition, but the output picture will be in the format chosen in the button right below the ‘placeholders’ checkbox.
In your image, one can see that the output will be PNG, in RGB+A format. If you want to change the output, you can click in the ‘PNG’ button and choose another format. 
Render cache path is set in user preferences -> file, check it there.