There is really very little in the way of similarities between realism and liberalism in how they would analyze the invasion of Iraq in 2003. The differences are much more important.
Realists would say that the US (along with a few allies) invaded Iraq in 2003 because it was in the US’s national interest to do so. In other words, invading Iraq would make the United States more powerful. The US invaded so as to destroy the regime of an enemy, take away WMDs that could be used against American interests, and maintain stability in a part of the world that is important to the global economy. The US had to invade because there are no international bodies that could force Iraq to give up its WMDs or to prove that it had already done so. Therefore, if the US wanted to avoid losing power, it had to take matters into its own hands.
Liberals might agree that the US would not have had to invade Iraq if there were international bodies that could force Iraq to comply with rules about WMDs. However, they would also point out that, under international pressure, Iraq had already gotten rid of its WMDs even if the US did not know that it had. Furthermore, they would say that the invasion of Iraq was unnecessary because the UN sanctions had reduced the threat that Iraq posed to the US.
Liberals would also say that the invasion of Iraq happened because Iraq was not democratic. One of the major tenets of liberalism is that democracies do not go to war with other democracies and are generally more peaceful than non-democratic governments. Democracies do not easily go to war because the people have a say in their government and will resist wars of conquest. They do not fight other democracies because they share values and are naturally friendly with one another. Liberals would emphasize that a major purpose of the invasion was not to control Iraq but to help it become democratic so that it would become a more peaceful country.
Thus, liberals and realists have very little in common with regard to this war. Realists would say that it was all about increasing (or at the very least maintaining) American power. Liberals would say that it was about spreading democracy so as to make the world more peaceful.
The link below has an academic journal article about various theories of conflicts and the Iraq War. It should be very helpful to you in understanding these issues.