<strong> = it requires bold emphasise
<b> = some text is bold for ****s and giggles (when bold adds no semantic meaning, such as breaking up a URL to make it visually easier to read, or because your branding has a normal word and a bold word)
Visually is there a difference? No. Browsers will bold both for backward compatibility. Screen readers however will read differently for <strong>, and continue normally for <b>. A valid strict alternative is <span> with a class... visually it can be bolded, yet semantically has no more meaning than any other words around it.

You can simple read the text... if when speaking you emphasise the word it should have <em> or <strong>, if you don't then it doesn't. Think a TV ad, it yells certain bits at you that is more important than the rest.