Throughout her early childhood my daughter was at the extreme end of the "sociable" spectrum, though as a preteen she seems to be becoming more average now. If you add up the numbers, the vast majority of her friends are not home educated. She's made friends at all of the following: local park, drama group, dance, chess tournament, music holiday club, swimming pool, choir, gymnastics, management committee of a youth theatre, residential sports camp, and Tesco(!). There are also friends of friends, my friends' children, and neighbour children. There are dozens of children she is quite fond of and sees occasionally.
However, the vast majority of time that she actually spends with friends, she is with HE friends. Her three closest friends are HE.
It just comes down to the fact that school friends don't have a decent amount of time to play. School eats most of their day, and prevents them from staying up late on a school night. In theory they might be able to play for a couple of hours a day - but in my dd's eyes, a mere two-hour playdate hardly counts anyway. In practice, there are so many other demands on schoolchildren's after-school time that by the time you account for homework, doctor appointments, shoe shopping, clubs and sports, it is not that easy to find a place in their diary at all. I have spent so much time chasing the parents of one particular schooled friend without success that I'm now giving up. I know they aren't trying to give us the brush-off, they are genuinely busy, but I'm tired of it. I've told dd that if she can pin them down to a given time then I am happy to accommodate them, but I'm not ringing them any more.
Contrast that with the two close HE friends who live within a mile of us. Often we don't even plan it ahead: we ring up - "Do your children want to come swimming with us this morning? If they don't have other plans today, we could give them lunch and drop them back to you at 5pm." Or dd will ring and arrange to meet a friend at a local park, and then they'll go back to whichever house they like. About half the time we get a yes. It's so easy. HE parents who are juggling a few other offspring, getting the loft cleared out and the laundry done are often very grateful to have one or more children off their hands for the day and may be delighted when we want to "borrow" children.
On top of that, I am slightly more keen on her spending time with HE friends because the friendships are likely to be longer-lasting. We don't have to make a special effort to keep in touch, as we do with school friends once the children move on from their choir and no longer run into each other. We bump into HE friends regularly at home ed outings. It has been lovely to watch these children grow up together and it's comforting to think they will have each other for years to come. In some ways it is like a cousin relationship. They have their ups and downs but there is an expectation of permanence in their relationship.