Многие из нас не умеют правильно поздравлять по-английски и используют слова "congratulate" и "congratulations" к месту и не к месту, в то время, как есть английское слово "greetings". Как правильно поздравлять по-английски можно узнать здесь.

The English language is at variance with Russian once again.
Whilst in Russian it is correct to congratulate people, not only on achievements, but on Birthdays and holidays, it is not correct in English.
In English, you send greetings for Birthdays, holidays, and events which are not an achievement:
I am sending you Christmas greetings.
Happy Birthday.
I wish you a happy New Year.

You send congratulations for achievements or when people have done something of note. Congratulations must be earnt:
Well done on passing your exams.
Congratulations! It's a boy! (Birth of baby)
Congratulations on your engagement.

The only exception is when somebody reaches a milestone Birthday or Anniversary:
Congratulations on reaching 100 today.
You are 16 today. Congratulations!