New Urbanism and Smart Growth
The New Urbanism believes in traditional urban design. Though it is a movement in city planning, it was founded by people who were trained as architects, not as planners, and who are primarily interested in creating attractive places. It has been extremely successful with the public because it has done such a good job of creating attractive places.
The Smart Growth Movement believes in transit-oriented develoment. It is promoted by people who are planners rather than architects and who are interested in quantitative abstractions rather than in designing urban places, so it tends to want as much housing as possible around transit nodes. It doesn't think much about whether this design will be attractive and popular with the public, because it relies on planning laws to get the designs built.
New Urbanism is compatible with Smart Growth. The sort of traditional development that New Urbanists want to build around transit nodes is a form of smart growth.
But Smart Growth is not always compatible with New Urbanism. The extreme wing of the smart growth movement wants to max out the square footage built regardless of whether it is good or bad urban design. Smart Growth planners sometines promote things like "point towers," which squeeze in more square footage but are not good urban design at all.
The ideas are generally compatible, and we all want to move in the same direction. The differences are in the details of how we move in that direction.
Unfortunately, because it does not focus on designing attractive places, the Smart Growth movement may build projects ugly enough that they provoke a backlash against transit-oriented development.