First one does look like honeysuckle. Don't know why it hasn't bloomed, unless the rosebush shades it too much. Second one is Greenbrier. It is the nastiest, most awful invader on the planet.

Dig deep and look for the tuber and the parallel root.

This is the first visible Greenbriar I've seen in this yard. So I'll watch it closely and go after it as specified on some internet pages with best instructions. Perhaps a bird just dropped it off recently. A girl can hope. :)

Keep your eye on it. It might take more than one attempt to kill it.

I'm thinking the top photos may not be Japanese Honeysuckle. After viewing tons of images of leaves of different strains of it on-line, NONE have as intensely indented heart shape at the base of the leaves as mine. None have leaves that look as thin and soft as these leaves are either. That, plus the fact it hasn't bloomed at all in two seasons with long runners clearly exposed to sunshine above the giant liriope and rose bush nearby, makes me think it is possible something else.

Sadly, there's no doubt that the blotchy one is Saw Greenbriar and I'll have to get on that before it gets established. One site said to lay a tarp on the ground to protect other plants from the chemicals and to lay it flat onto the tarp and glyphosate the thing several times over a week or so. But since this one is so young, just one 13" shoot, and has appeared nowhere else in the bed or yard, hopefully it' has not developed a deep, underground root yet. I may try to shovel it up first (liriope and all) and kill that "sucker" in its infancy. I just planted that liriope last year and it should come out easily. :)

It probably came in with the lire since this is not a fresh seedling. They are much smaller.. I am on seedling patrol as I speak and shamefully I have let some get away from me in my bamboo muhly patch. A runner has embedded itself in a groove in a tree. I have work ahead of me.