It depends how a person speaks. To say I live close to the sea, would have the meaning of living very close to the seaside, you can see the water, so to speak. Whereas, I live near the sea, also has the same meaning but does not have to be right next to it, you can be a few kilometres away from the sea and still live near the sea. Also, if your telling somebody from the countryside that you live near the sea/close to the sea, it does not really matter which expression you choose.

There's no big difference between using "close to" or "near" other than the amount of words used. They are synonyms(mean the same thing) so you don't have to worry (￣▽￣)