Hi! Newbie here! Walking my backyard, I noticed two plants I haven't seen before. (Which is odd, I've been here 10 years!)

I'm not sure what they are, please help!

The first seems like a vine, or else mounding. I noticed it along my wire fence and in shady, woods spots.

The second I saw also in the shade along my fence and in the old leaf piles. It's like ground cover with pretty green leaves and tiny white flowers.

Do I have weeds? Are they worth transplanting?
Thanks for your help

Ps - in New Hampshire