"tell" = personal and direct
"inform" = formal and neutral
You may tell someone almost anything. For instance, you may tell about your day, tell a story, tell someone to do something, etc.
You may only inform someone of official facts. You would not "inform" someone about your day (unless you were merely giving them facts without your opinions). You may not "inform" someone a story or to do something, etc.
Example 1:
"I INFORMED my sister about our mother's condition in the hospital."
This means that I told her the facts: "Mom is in the hospital. She broke her leg. They are putting a cast on it for about six weeks."
"I TOLD my sister about our mother's condition in the hospital."
This means that I added personal details or my opinion: "Mom fell down the stairs. You know that back porch with the loose step? Well, it broke right under her. She was a trooper though! I'd have been screaming in pain! Well, anyway, the doctor set it and now she'll have a cast for about six weeks, so you and I will probably have to drive her places."
Example 2:
"I TOLD the neighbors to keep their dog quiet at night."
I told them TO DO something.
"I INFORMED the neighbors that, if they did not keep their dog quiet at night, I would call the police."
I informed them of FACTS. It is implied that they must do something, but the fact is this: "If you do not do X, I will do Y."