Intimidate usually means to scare someone or make them feel uncomfortable by making yourself seem bigger, scarier or better than the other person. This is done to make you appear superior. It is usually not as serious. Threaten is when you tell someone about your intentions to harm them in some way. This is usually more serious and the person's safety is in question. For example: If someone is much taller than you, you might say they intimidate you. If someone tells you "I am going to kill you", they are threatening you.

Intimidate : it's to scare someone into doing something you want them to do. They are many ways of intimidating someone, by actions or words. A threat is to directly scare someone for whatever reason. It's harshly communicated Example intimidation : hi John, I hear you asked my girlfriend out for a movie? Last time someone did that, I was not very happy. It did not end well. Example, threat: hey John! I hear you asked my girlfriend out for a movie! Last time someone did that, I wasn't very happy! It did not end well! The difference is the tone. Check the exclamation marks! This means the conversation is hard and threatening.

To expand on Nikky's response - if someone says they are going to kill you they are both threatening and intimidating you. The differences are very subtle sometimes and you'd be best finding some examples in context to fully understand the differences.