Unschoolng is a type of homeschooling where we don't follow a curriculum. Homeschooling still very much exists.
I first came across unschooling in 1991 via "the Teenage Liberation Handbook (how to quit school and get a real life and education)" by Grace Llewellyn. The updated 30th anniversary edition came out a few years ago.
Wonderful book, I've given out many copies as gifts. Often it can be found online as PDF.
It sounds like Unschooling is what used to be called Deschooling 50 years ago[1], and is very different from homeschooling in that homeschooling uses a government prescribed curriculum that is administered by parents/guardians but is still pretty much the Prussian model of education, at home. The Prussian model is essentially geared towards creating good little workers/consumers with little critical thinking skills, whereas this mode of education is more fluid, to say the least.