I find the distinction interesting... and once had a very long chat with a very smart anarcho-communist.
After days (and page upon page) of discussion, we realized that so long as neither of us is willing to resort to force or violence to impose our property views on each other then it really doesn't matter. We will just tend to form our own communities.
Most people I meet that are against capitalism are against what I'd call crony-capitalism and not true free trade.
Most people I meet that are against communism are against centrally controlled communism and not shared property.
As for me, I dropped the ancap label a while back simply because as long as we agree on (a) no rulers and (b) no force then any other differences we might have probably aren't worth worrying about... at least not until we live in a free world.