SAT I is the Scholastic Aptitude Test that is now known as the Scholastic Assessment Test. The format of SAT I has changed in recent times, with certain additions and subtractions.
The SAT II was called the Achievement Test in the past. Some very highly competitive colleges and universities require three SAT II scores, and for such purposes, one would find it necessary to appear for this examination. On an average, the three SAT IIs required are Writing, Math, and a Science or a Language of your choosing.
The SAT II test tests how much of a certain academic subject you have learnt in the span of a year; and the right time to take this exam is the end of your junior year in school.