Homeschooling is interesting. In certain states in the USA, the schools have a program that they put out where its the school work from the state/school, but it’s designed to do at home. I don’t think of that as true homeschooling even though technically it is.
There’s another kind of homeschooling which is what I did. My mom ordered the curriculum off the internet. (you can get examples from christianbooks.com.) When the books arrived, we worked through them at my own pacing and eventually, when I was done, she’d order more.
My curriculum was from a Christian worldview (which is one of the reasons I was homeschooled). Even though my history and geography and etc. was Christian, math is still math. Spelling is still spelling.
I had tests, but none of the final end of the year state testing that we have here. I was fortunate to escape that. We didn’t have to register with the government although I know some states do (California) and some countries do.
Some people look down on homeschooling because we “don’t get a good education”. That’s nonsense. I have as good as an education as those around me. I may struggle with some subjects, but don’t we all? (spelling I’m looking at you. Thank goodness for spell check lol)
Another thing people criticize is “You don’t socialize!” Well, I lived in a remote, national park for 5 years of my life. I couldn’t socialize with people my age because there weren’t any! And the few that were there, didn’t like me because I was different than them. I socialized with adults. In fact, I still get along better with adults than I do with people my own age. Just because I didn’t socialize in a school and in a somewhat forced environment, doesn’t mean I have all the social interaction I need.
This got much longer than I thought it would, but I hope it answered your questions. Let me know if you have any more questions!