I know there is a difference, but I can't put it into words.
ADDENDUM: I know that soldiers nowadays can't wear their uniforms out in public as much as they did back then
The short, simple answer at least in respect to the conflicts that went on in Iraq/Afghanistan over the past decade is the concept of total war.
The concept of total war means the belligerents engage in a complete mobilization of all available resources and population. This includes and is not limited to the civilian population and collateral damage towards the 'enemy.' World War II is probably the greatest modern example, as every nation involved had one purpose and one purpose only: war. There was direct targeting of civilian populations, and collateral damage was usually not considered.
Now, there is a general trend against total war. Most nations now that go to war, it's only a small facet of what is going on. You can also see this in the "hearts and minds" campaigns that go on in our military incursions. Collateral damage is something that is generally avoided (or at least there is an attempt to avoid it), and direct targeting of civilians is also greatly shied away from.
This question is a little vague, it might help if you were more specific. Different in terms of weaponry, economics, social views thereof...?