That is still an improper definition of communism, but let's have a look here.
"Communists remove the physical trade of goods" you say. Well, they intend to and they have had partial sucesses, but they never fully succeed because that would be impossible. What they do is try to prevent certain kinds of "trade".
"free trade and free association are essentially the same thing" Well they are connected, but not the same. However, as you pointed out the "communists" "remove (physical) trade of goods". How they "remove" such trades and why, is why they are called socialists.
Anarcho-Capitalists don't necessarily want to run a bussiness, work for a traditional employer or work the land. -- They can be part of a cooperative if they want to and they can enjoy welfare services as long as they are not at the expense of someone who didn't approve of them. As long as they don't oppose the freedom of trade, they are not socialists. A "Capitalist" must not necessarily desire trade or contracts in all ways they could possibly take place.
Still though, I do like the fact that you made an effort to compare the systems and that you found similarities. Because there are similarities and I know this, because I used to be an "Utopian" socialist and later became more of a Marxist radical; So I've seen "both" (that's an extreme oversimplification of course) sides.