Thyme or tarragon? I'm not sure.

[splash79]

Last year, I decided a bit too late in the season to grow some herbs other than basil. I grabbed some window boxes, tossed in some seeds, and waited. Long story short, I don't think I planted enough seeds, because there wasn't really enough to harvest. I chalked it up to an experiment, was happy things grew at all, and figured I'd do better this year.

I was cleaning out the window boxes yesterday and found that a third of one of them was FULL of roots (the entire chunk of soil lifted out of the box). Just as I was getting ready to pull it all up and toss it, I noticed some tiny green and red shoots sticking up.

Before I noticed what I'm assuming is new growth, I pulled out the old seed packet markers and just tossed them to the side, so I have no idea if this is thyme or tarragon. i also pulled out some old stems, which are about 16 inches tall that have "shoots" coming off of them that are about an inch long. Based on that, and looking online, I think it might be tarragon, but I can't be sure.

I took a picture of the new growth , if it is actually new growth, just in case someone here is awesome and could tell what it might be based on that. If it is growing, should I transplant it into its own pot? The area with the roots is about 6x6 inches and, while I didn't pull it all the way out of the box, I suspect it might be rootbound.