Sarcasm (noun) is to say the opposite of what is happening at the time. It is as a type of humour, usually used to make fun of someone. For example, you see your co-working sitting down reading the newspaper and drinking coffee, so you say: 'Wow! You look really busy!'
When someone says something to you which is rude, they are being offensive; you are offended (you are shocked and angry). When we take offence to what someone has said we use the following phrases to let the person know that we are not happy with what they said: