I wanted to know what are two similarities and two differences between our involvement in Vietnam and our 2003 involvement in iraq.

This is a very powerful question whose answers will have
to examined through the lens of political affiliation.  On one hand, some differences
between both conflicts would be that the military escalation of forces is not the same. 
In Vietnam, the conflict experienced a wide escalation or swelling of military personnel
before a deescalation.  In Iraq, this is not present.  The President has committed to
withdraw troops with somewhat of a timetable, but the noticeable escalation of military
presence that was such a part of the Vietnam war is not there with the Iraq conflict. 
Another major difference is the casualty count.  Any and all loss of military life is
extremely painful for which to account.  Yet, the casualty number in Iraq is nowhere
near the count for Vietnam.  When such a number far exceeds 50,000, the situations are
not entirely the same.

Some similarities are present.  The
first would be that the wars experienced an increased in unpopularity.  The Iraq
Conflict and Vietnam Wars were and are unpopular.  The large scale of increased support
from the body politic are not as present in analyzing both conflicts.  Another
similarity would be that each conflict proved to be more difficult than originally
envisioned.  The Vietnam Conflict was seen as the mighty power of America against a
"bunch of people in black pajamas."  Yet, once the war had continued, there was a
distinct complexity that forced America's hand in being trapped between options that
were undesirable.  The same situation presented itself in the immediate stages of the
Iraq conflict.  The notion that America would be "greeted as liberators," that there
would be an immediate reality of a lower price of oil, and that once Saddam Hussein
would be removed from office, democracy could take a quick hold were all false
assertions.  The removal of Hussein and anti- American fervor that developed ended up
allowing multipolar tensions to surface, making "the enemy" that much more difficult to
identify.  Additionally, the removal of Saddam Hussein actually helped to allow Al-
Qaeda operatives to enter the region, causing even more
instability.