Most states, including NH, consider distance (online) learning as homeschooling, even if it is full-time in an accredited program. College Board, the organization that issues the SAT exam and Advanced Placement program, follows this same standard.
Full-time enrollment in the Virtual Learning Academy Charter School (VLACS) is not homeschooling as it is a NH-based chartered public school. However, students are considered homeschoolers if their enrollment in VLACS is part-time.
There are thousands and thousands of online education providers. Some offer individual classes while others offer entire curricula across grade levels. You can find many listed on our High School & Beyond page.