Things can get a little confusing with Acrobat because there are two options to save a PDF file in this particular context: you can either save it as a "reduced size PDF" or as an "optimized PDF". As one professional illustrator puts it, the first option is a "quick and dirty approach." The better way would be to save it as an optimized PDF because it gives you more control over the optimization, downsampling, and other technical parameters, as shown below: