Yeah, the definition of what ‘strong emphasis’ is compared to just ‘emphasis’ is pretty woolly. The only standard definition would be “it’s emphasised, but more!!”.
Personally I use <em> for normal emphasis where you’d read the emphasised word in a different tone of voice, and <strong> for that thing where you take key words and phrases to pick them out of the text to help people skimming the text pick out the subjects.
This isn’t a standard interpretation, but it makes some sense and rendered appropriately by the default italic/bold styles. Whatever you do, be consistent.