Public Law
A public law is one that has passed through Congress and been signed into law by the President. It is assigned a law number and is published as a slip law. Example: the Patient Protection and Affordable Care Act is Public Law No: 111-148; it is the 148th law passed in the 111th Congress.
Statutes at Large
The Statutes at Large permanently compiles all the public laws passed in a session of Congress, so the laws are arranged chronologically in each volume. The citation reads volume number, name of publication, and page number where the law begins. Example: the Affordable Care Act is found at 124 Stat. 119: volume 124 of the Statutes at Large, page 119.
The United States Code gathers all the laws and arranges them by subject matter into a Code with 50 "titles" or subject headings. Title 42 is for Public Health and Welfare, the title where you will find many health and social work-related laws. The Affordable Care Act is codified into the U.S. Code at 42 USC 18001.