I've known the Russian word "много" for some time now, "намного" a little less long, and "гораздо" only very recently. I am now beginning to wonder if there are any subtle differences between them or any situations in which you would not use one or the other(s). As far as I can tell, of the three, "много" is, far and away, the most common, followed by "намного" and then "гораздо." Also, are any more formal/colloquial than the other(s)?
"Много" means both 'many' and 'much' when they are used before nouns, in Russian there's no difference between these two words:
много друзей - 'many friends';
много денег - 'much money'.
On the other hand, "намного" and "гораздо" both mean 'much', but not in the meaning I mentioned above. They are used before adjectives in the comparative degree and mean enhancing the quality named by the adjective:
намного/гораздо сильнее - 'much stronger'
намного/гораздо быстрее - 'much faster'
намного/гораздо больше - 'much bigger', 'much more'.
There's practically no difference between "намного" and "гораздо", they are practically complete synonyms, but their difference from "много" is substantial. As for me, "гораздо" sounds a bit more colloquial than "намного" which is neutral, but that can be subjective. And you're right, "намного" is used more often than "гораздо".
Just to add up something to the given answer. While "гораздо" and "намного" are indeed almost identical, sometime first word is more appropriate to use.
It's better not to use "намного" with words with the same root and antonyms.
So forms like
гораздо многообразней or
гораздо меньше are preferable compared to
намного многообразней - this sounds tautological - or
намного меньше - this can sound confusing.