definitely stiltweed. I have tons of it around the property here. Our lawn was neglected for a couple years before we bought the house and it took over the lawn. Every summer it would burn out and leave patches of dead stiff stalks. When our landscapers did their fall cleanup it would all blow out and leave bare patches. Our lawn company never figured out what it was in the 2 years I was trying to get them to sort it out. This was the grass that started me on my lawn journey. I decided to take over all of the weeds and nutrition for my lawn at that point.
Stiltgrass spreads through seed but also through stolon. It grows quickly so getting it early is the key to control. In the lawn I think I have it mostly squared away now. Around the edges (we back up to woods) I try to spray all of the perimeter with glyphosate a couple times a year to keep it knocked down. It still comes back, but it doesn't spread into the grass so much.
If you have an outbreak in your lawn you can manually pull it if its not too much. Or, you can spray. Glyphosate works if you can manage the patches. Alternatively Acclaim from bayer works. Its pricey but it works if you're a sprayer. For the first picture, I'd start by hand pulling all of the tall and thick stuff by the fence. Tough to tell but it looks like there is a lot in the yard by there as well. If its a thick as it looks, I'd glypho the yard there and kill it off now. Its the right time to be seeding and its easier to nuke the whole thing than try to be selective.
