Yes you're right CIG is stating their "product" is in Alpha, FD is not. It's you who is stating that ED is in alpha/early access. This assertion (if you even believe it yourself) is merely your opinion.
I think the difference is that FD is confident enough that their product stands up on its own merits and is of merchantable quality where as CIG would be laughed out of any room if they tried to claim their lavishly funded efforts were an actual merchantable product as opposed to the in-progress mismanaged mess that it is, hence the alpha/early access fig leaf.
However that is merely my opinion.
If someone decides to call an elephant a snozzleear (LOL) that does not reclassify the nomanclature.
ED is unfinished
ED is bug ridden
ED is still adding features.
In fact, you could safey say neither game is even in Alpha state yet because they lack many of the key features that will go into the finished product.
As I understand it, SC is not early access because, if I buy the $45 package right now, I won't get to play it? ED on the other hand is just like The Forest in that I can play the game, it has tons of features already but is still early access as it's not finished. The devs of the Forest call it an alpha build, just like the devs at BIS call DayZ an alpha build.
We've already heard from FD how they're new to this kind of gaming. BIS are not new to any kind of gaming and can recongnize an alpha build when they see one. Therefore, given all of that I think it's safe to say ED is an early access game that's currently in alpha awaiting the compeltion of features and the many bugs the game has, ironed out. Some of those bugs include,
The PowerPlay fiasco
MP netcode
Missions
AI
Interdictions
This is why I call it alpha state and early access