Part of this is due to the fact that home schooling tends to be the American term (where HE is more prevalent than in the UK), and part of this is due to ignorance. [Note: I mean ignorance in the genuine lack-of-knowing sense, as opposed to meaning rude and purposely using the wrong terms.]
But does it make a difference?
Personally, I think it does. I think words matter and home schooling has a totally different connotation than home education.
I home educate.
I educate my youngest (as DD1 is now in school).
I facilitate her learning.
I encourage her when need be, but generally her own innate curiosity is such that she is learning all the time.
I don't teach her (though I do when she specifically asks to learn something specific).
I don't school her.
I don't make or encourage her to learn as they do in school.
I don't train her or lecture her or coerce her.
I allow her to learn at her own pace, what she is interested in, for as long as she is interested in it.
But isn't it just semantics?
Yes and no.
Thesaurus.com has 'schooling' listed as a synonym of 'education' so in some ways it is no surprise that the words are used interchangeably.
The problem arises when people who don't understand HE use the term 'home schooling' and infer, wrongly, that HE should recreate school. This is especially a problem if the person using the wrong term works for the LA as an EHEO.
We know that legally, Section 7 of the 1996 Education Act states:
Duty of parents to secure education of children of compulsory school age.
The parent of every child of compulsory school age shall cause him to receive efficient full-time education suitable—
(a)to his age, ability and aptitude, and(b)to any special educational needs he may have,
either by regular attendance at school or otherwise.
There is absolutely no requirement for us to recreate school-at-home, and if you look at my posts from last April, you will see that even with the new guidance, that has not changed.
As more and more people start to home educate, the world is getting more political as some in the government try to rein us in. We need to keep our freedoms and using terms such as 'home education' can really help.
As many EHEOs already don't understand valid home education approaches, such as unschooling, it is of upmost importance that we keep reiterating to them that we 'home educate' and not 'home school'. Children do not have to be tied to a table in order to learn. Children do not have to be kept inside in order to learn. Children do not have to be kept away from the rest of society and arguably from real life, in order to learn.
Language evolves, and the more often people use certain words of phrases, the more prevalent they will become. As home educators, I think it is our responsibility to use the correct terms that encourage an opening of the mind to wider possibilities, rather than using an allowed term, that encourages the mind to close and focus in only one direction; especially when discussing with the LA.
In your own homes? With your own friends? Use whatever phrase you want, but if you say 'home schooling' around me, I will be privately miffed.
(There are other terms that home educators also use to convey their educational approach, such as Life Learning, Life Education, Education Otherwise, and many more which try to show the wider scope of education than simply 'school'.)
A couple of blog posts from other people (2012 and 2016) that also talk about this topic:
Home Schooling Vs Home Education
Forgive the Homeschooling