It isn't a question of politeness. In fact, the first is unnatural - we would normally say the second in modern English: 'She is two years older than me'. The only time it is normal to use 'elder' as an adjective is before the noun, usually to describe sibling relationships, for example, 'She is my elder sister'. 'Elder' has come to be associated with seniority, which is why it is used in this way. If you are unsure, the easiest option is not to worry about 'elder', and never to use it. You can equally well say 'She is my older sister'. It is never necessary to use the adjective 'elder', as 'older' will always be correct.

Another important distinction between these words is that 'older' is a comparative adjective and elder is not - older is used to compare the age of one thing to another - "My brother is older than me." So your sentence "She is two year older than me" is correct. Elder is never used as a comparative adjective, it is descriptive only. "My elder brother will help us." It describes its object noun as being older than the subject but is not making a direct comparison, as in 'he is older than her'. 'Elder' is also used as a noun, as in she does not respect her elders." Hope that helps.

"She is two years older than me." That is the correct sentence. It has nothing to do with being polite.

Hi Hard, actually I just had this question how English-speaking people feel this difference shortly before. I think we have some feeling about the word "old" both in favorable and unfavorable senses in Asia.

Incidentally, your question should start with "Is", not "if".