If we're talking geology, then we might as well look at the tectonic plates [0][1].
- 14 or 15 major plates
- 38 small plates
Yet people will talk about 5-7 continents all the time.
Because people will be confused no matter which ill-defined definition is used, I'm switching to the botanical one [2] with 9. It seems to at least have some practical value.
[0] https://en.wikipedia.org/wiki/Continental_plate
[1] http://peterbird.name/publications/2003_PB2002/2003_PB2002.h...
[2] https://en.wikipedia.org/wiki/Continent#Botanical_continents