PPI (Pixels Per Inch, which are different from Dots Per Inch) will decide the number of pixels in the exported image only if you set the Image Sizing measurement unit to inches or cm instead of pixels. If you stick to the default of pixels, it has no effect whatsoever. The only reason for showing physical units on that dialog is to help you do the math.
PPI is a tag in the JPEG header which tells third-party software how to calculate the "100%" physical size of the image, for example when placing it into another document or starting the page setup for a printout with "use actual size" selected. It doesn't affect image quality, sharpening, etc. in any way. In the attached 100% crop of some laser engraving, the left side was exported at 1200PPI and the right side at 12PPI (print sharpening enabled).
When printing from any pixel-based format, the image size (in pixels) and the scaling factor (in percent) are all that matter. If you export a 1000x1000 pixel JPEG file at 300PPI, and another one at 30PPI, then use 'fit to page' when printing, the result will be identical. However, drop them into a Word file and the second one will be zoomed like crazy.