J-1 visa is known as an exchange visitor. These visa holders participate in a program, which aims to promote cultural exchanges between the two countries. It is monitored and the department of state accepts exchange visitors and programs into it. Many programs require that the exchange visitor return to their home country for a minimum of two years after the program has ended in order to pass along the cultural learning.
See the state department website for more information: http://travel.state.gov/visa/temp/types/types_1267.html

F-1 is a student visa that allows foreigners to enter into certain levels of study in the US, including public high school, provided they have enough funds to pay their tuition fee. Attendance is limited to 12 months for a public secondary school. So, if you want to spend your entire high school career in the US, you would have to attend a private institution.
See http://travel.state.gov/visa/temp/types/types_1269.html for more information.