There are lots of avenues of public service. If you want be counsel for charitable organizations and help them get incorporated and all that stuff, that is one option. You could also be an attorney for legal aid or a public defender (or proecutor for that matter).
I'm probably missing a ton of public service things but the main point is that public interest law is not so much a type of law as it is a career choice. As a public interest lawyer you can do most types of law (criminal, civil, tax, bus org.) it isn't very limited.
So public interest usually involves serving:
1. the poor
a) private organizations that live off of charitable donations
b) public organizations that work for the government (public defender)
2. the government
(b) civil stuff in government agencies
(at this type of job you could be working on vidicating individual's rights - working for State AG civil rights division- or denying them when the state is sued- trial division of state AG. There is alot of variety.)
3. working as counsel for non-profits.
Differences with firms. Many of these type of jobs do not require you to bill your hours or work 70 hours weeks consistently. Also the huge thing is that you get more experience quicker. In some big firms, you will work on discovery for 4-7 years without ever handling your own case. At an ADA or defender position, you're in court immediately.