You would think they would be pretty much the same, wouldn't you? Both involve academic schoolwork type activities, both are done at home, both sometimes require the help of a parent... not much difference between them it would seem. Yet, if homeschooling were even remotely like helping with homework, I'm pretty sure we wouldn't be homeschooling... especially with 6+ children.
You see, despite the seeming surface similarities, they are really very different things. (Thank goodness!) Let's take a look at each one. Homework is something sent home from school by the teacher. (Though I'll show my age and point out that when I was in school, homework was something you took home because you didn't finish your work in class. I'm pretty sure I never had specifically assigned homework before junior high.) It also means that it needs to be done after a child has already spent 6+ hours in school. I think it's pretty safe to say they are not at their peak at this point. Homework is also assigned by the teacher for the whole class and not restructured for each student. Usually the parent has no say in whether all the homework should be completed. (I did have a friend when M. was little who would send her daughter's homework back undone with a note saying it was pointless and little more than busy-work, but I'm not sure she's the norm.) Can you tell I think the whole homework-thing is a little wrong-headed? My local school district should thank me for not sending my children to them, because I don't play well with others and would be that parent, I'm pretty sure.
How does homeschooling differ? Well, the biggest difference is that when we work on academics, it is during my children's freshest time of the day. For most of them, this is morning time. They haven't sat in a classroom for six hours already; their brains are ready to concentrate. I get to decide what each child is working on. I know them quite well and know their strengths and weaknesses. One child may really need pages and pages of math problems to do to cement the concept, while another can grasp the idea and get them right after just a few. If a child is having a particularly difficult day, we can drop the academics entirely and save it for a better time. If a book just isn't working for a child, I can change the book. I have the luxury of being able to tailor my children's education to each of them. Plus, by homeschooling, I also get to experience the fun and joy of learning with my children. I get to help them do the big projects and cool experiments. I get to hear them discover how to read. I don't just get the dregs.
Plus, we are done by lunch (well, most of us, the high schoolers spend more time on academics, but they are older.) My children have time to rest, play, read, or whatever after lunch, and then that leaves time for other activities in the afternoon. When their father gets home from work, we can enjoy each other's company without having to worry about getting homework done.
I've had many, many people tell me that they are sure they couldn't homeschool because helping with homework is such a nightmare. I tell them I couldn't do traditional school because homework is such a nightmare.