In the US, 2-year colleges offer associates degrees. 4-year colleges and universities both offer bachelors degrees. Universities also offer masters, PhD, and other programs (med, law, etc). Some colleges are better than some universities and some universities are better than some colleges. Colleges tend to be smaller, private, and offer fewer programs.
An undergraduate student is working on their bachelors degree. A graduate student has a bachelors and is working on a masters or PhD.