When I look at the first picture, "lamb's quarter" pops into my head, but I really have no idea why. I don't think I know what lamb's quarter looks like.
(I sometimes amaze myself with what I know and didn't know I knew. Happens all the time when I watch Jeopardy)
That first one looks like my lambsquarter here. Mine mostly ignore it, but every once in a while the SA leopards will eat some. The second one is filaree. All of mine eat that. At this time of year I go around with a bucket and scissors and chop up all sorts of weeds. I don't throw lambsquarter in the mix, but I do throw lots of filaree in.
I love this time of year. 80 degree days and all the delicious nutritious weeds my torts can eat.