Help me identify these plants?

[WilsonFarm]

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


Ps - in New Hampshire

[faladinda]

hi..
in first image, is that Evergreen candytuft ? i was trying to search the first image and i get this :
https://www.finegardening.com/plant/evergreen-candytuft-iberis-sempervirens

and actually that flower seems very familiar to me, i barely find that kind of flower but i have seen that flower in some wedding event on TV.

may it helps you, but i have no idea for the second image :(