Hugs,
Just to echo what apg said, public health encompasses a number of different fields, including epidemiology, health behavior/education (which may or may not include community health), health administration and policy, environmental and industrial health (including toxicology), international health, and tropical medicine. These concentrations exist at most schools in various forms (for example, health behavior may be found in Columbia's Sociomedical Sciences Department, while International Health exists within the Epidemiology department (not standing as it's own) at Michigan.
Most public health programs will provide you with a good solid education. If you want to know more about specific schools, call the departments of interest at the schools you're thinking of applying to and see if you the personnel could give you the e-mail addresses of current students (or have them tell you the types of jobs of that alumni are doing).
Public health is about protecting the public's health through education and research. There is really no distinction between public health and community health, as the community is what makes up the public in public health. This is why I, as many of my colleagues will echo, love this field - for its all inclusiveness with regard to an individual and the factors that affect their health status. There are many undergraduate institutions that grant health education or community health degrees, but I think that you'll find most graduate programs in these areas will grant the MPH degree (i.e., the MPH in Health Education can be obtained through the School fo Education at NYU, which is an accredited program with no affiliated School of Public Health). Depending on what you want to do, I don't think that one degree is better than the other. Just consider the MPH because you receive a comprehensive education that allows you to explore different aspects of public health - not just the area of concentration.
Best,
H&T