I was reading in the law library about the non-statutory motion to vacate is treated as a writ for coram nobis by the California supreme court, but the author argued that the non-statutory motion to vacate was the only judicial mechanism for remedying a Constitutional defect out-of-time. I didn't know you could write, "Non-statutory motion to vacate plea" on a motion, but looks like some people have, but the California Supreme Court still treats it like coram nobis and denies on IAC.
Does this happen in other states?
You are asking a very difficult question. If you are trying to vacate an old conviction you have limited options, you can try to get a certificate of rehabilitation. You should contact a lawyer and explain what your prior conviction is for and what your goals are - in other words why you want to clean up your record. Some public defenders offices will accept appointment on these kinds of cases so, if you qualify, you could get a free lawyer to help you. This is a pretty techinical area of the law and you should get professional help.
There is no such thing as a Non-statutory motion to vacate. People have tried to invent such a thing and, like you said, courts have treated it as a writ of error coram nobis, which is indeed the only way of addressing a constitutional violation that took place in the trial court, once time for appeals and custody for a habeas petition have run out. And, you can't raise IAC on a writ of corm nobis.
The question that you ask inquires about California procedure, and the answers you have received address the law of that state. Collateral remedies vary widely from state to state and in many respects California procedure seems rather unusual. The entire subject of collateral review is, as has been pointed out, very technical and complicated and federal remedies are the most complicated of all. Not an area for a novice.