Word mean different things to different people. Why?
Why do the same words mean different things to different people?
People get perplexed because they may say something (a word, phrase or sentence) to one person and get one reaction and say the exact same thing to anther person, and get a completely different, or even opposite reaction. Don't words mean what they mean?
There are actually two distinct meanings to words and language. The first -- the denotative meaning -- is the one you are most familiar with. It refers to what the word refers to. For example, the word cat's denotative meaning is an animal with four legs and paws, a tail, whiskers, etc. (there are obviously exceptions). While there are some differences between people on what they believe a cat to be, usually there's little agreement. When you talk about a cat, most people will understand what you are referring to. That's not where the differences usually come from.
The second type of meaning is called the connotative meaning. The connotative meaning of something has to do with what the word suggests to the individual, based on that person's experiences and emotional reactions and judgements associates with the word or what it refers to. Let's take the cat example.
Two people may understand what the word cat denotes. However, one person may have grown up around cats and learned to enjoy their company. The other, however, may have been attacked by a cat when young, and so s/he associates the word cat with very unpleasant emotions and judgements. So, the meaning of the word cat (in terms of it's associations) is different for each of those people.
So, when you say "I'm bringing my cat to your house", one person may be pleased and react positively, while another may become angry and yell at you that you certainly are NOT going to bring the cat.
Think about how the words "Republican" and "Democrat" affect people differently. Those different reactions have to do with the connotative meaning of those words. Two people may understand, in objective terms what each of those word means, but what's most important is that those two words have different connotative meanings, and those differences explain why some people may react negatively to one or the other of those words.
Understanding that connotative meanings differ from one person to another helps to reduce conflict that stems from differences in those meanings, and explains why people react differently to the exact same words.