The HTML Strong Element is used to markup strongly emphasized text.
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I <em>may</em> want to buy the update. The website was <strong>awfully</strong> flawed, it had <em>several</em> security risks.
The above might not be perfect examples, but it should be enough to convince you, that there both are times where you would want a word to be strongly emphasized, or less emphasized using em.
As far as I'm concerned, there is no right or wrong, it will be up to the Author, or writer of a given article / text, where to place the weight on the words. Lets take one last example.
<em>Note:</em> Don't emphasize to much, that way nothing will appear to be emphasized.
Generally anyone will know when to use emphasized text. Simply using it, where you normally put the weight on your words, is a good rule, and rarely needs to be corrected.