Both are quite similar by means of "accomplishing". But "realize" has a sense of constructing, bringing something into REALITY. While "achieve" stands for reaching a certain goal or overcoming a difficulty. "English anf French people realized the incredible task of drilling the tunnel which now connects the two countries." "The cure for some types of cancer is one of the objectives that modern medicine hasn't achieved yet"

Realize is to come to understand. Achieve is to gain something positive generally through hard work.

The difference between realize and achieve = realize means reality and achieve is accomplish. Examples to this words are: (1) I realize now what I said yesterday was wrong. (2) I'm so happy I achieve my goals.

When I realize my goals, I will have achieved some personal satisfaction....

Examples: a1) It seems me that you did not fully realize what happened yesterday. b1) Maybe you could tell me what you think about that a2) If you keep on changing your plans every week or so, you might get some fun, but hardly you will achieve something real. a3) I don't want to take vacation this summer, I'd better study and try to achieve University's admission in September. a4) If the only thing you want to achieve in life is success, than probably you are on the wrong path; success is a side effect of other achievements. a6) sometimes we realize that since childhood our will was set for the very same achievements as in adult life. I consider this a lucky circumstance.