What is the real accounting on the Iraqi refugees?

I'm on this topic because yesterday the New York Times ran a story about Iraqi refugees in its magazine section. Nir Rosen wrote:

At a meeting in mid-April in Geneva, held by António Guterres, the United Nations high commissioner for refugees, the numbers presented confirmed what had long been suspected: the collapse of Iraq had created a refugee crisis, and that crisis was threatening to precipitate the collapse of the region. The numbers dwarfed anything that the Middle East had seen since the dislocations brought on by the establishment of Israel in 1948. In Syria, there were estimated to be 1.2 million Iraqi refugees. There were another 750,000 in Jordan, 100,000 in Egypt, 54,000 in Iran, 40,000 in Lebanon and 10,000 in Turkey. The overall estimate for the number of Iraqis who had fled Iraq was put at two million by Guterres.

But now consider what Human Rights Watch reported in February 2003, a month before the U.S.-led invasion:

As of late 2001, between one and two million Iraqis living outside Iraq were thought to have a well-founded fear of persecution if they returned.⁷¹ Of these, only about 300,000 had any formal recognition as refugees or asylum seekers, largely due to the failure of the governments hosting them to put in place refugee status determination procedures. Instead of providing for their needs, many of these host governments imposed hostile policies aimed at restricting refugee rights so as to deter additional Iraqis from entering their territories.

I've been wondering about this issue since I started reading recent press accounts of the numbers involved.

How did all these Iraqi refugees get absorbed so quickly - and so silently - in such relatively small and poor countries like Syria and Jordan?

Did I miss the coverage - not to mention pictures - of these two million Iraqi refugees fleeing Iraq after the invasion?

And did the two million Iraqis that fled Iraq under Saddam come home and then another two million Iraqis left?

Or are they still the same two million refugees?

Could someone help me square these before and after numbers?