The difference between "bad" and "badly"

As I  say the other day, I'm constantly looking for inspiration and new interesting stuff. I just found one of these interesting things in the writing niche, in a blog where is explained the difference between "bad" and "badly". I think I know the difference and would have use the proper word without actually knowing or thinking too much, just after the way it sounds. I'm not an English native, so this article is of a great help. ;-)

The text article:

Here’s something that writers often mix up. When you use verbs that express a state of being rather than an action, like become,feel, seem, smell, sound, taste, you follow them with an adjective, so they are not treated like adverbs. Do you remember the rule about adverbs—they usually have ly at the end? Here’s how you use these types of verbs:
I am fine, he became sad, she feels bad [not badly], they felt ill, you seem happy.
If you say “the fish smells bad,” you mean it stinks. If you say “the fish smells badly,” it means the fish has a poor sense of smell.
If you say “I feel bad,” it means you are sad or sorry. If you say “I feel badly,” it means your fingers are not very sensitive and you can’t tell what you are touching.
If you say “I look different than you,” it means we don’t look alike. But if I say “I look differently than you,” it means my way of looking is not the same as your way.