The two photos above are both of the same moth, which I think is a Bluegrass Webworm Moth (Parapediasia teterrella). The smoothly curving subterminal line and toothed post median line are distinctive. These moths are found in grasses; you may flush them (or their close relatives) as you walk through a grassy field or lawn. According to BugGuide, the larvae feed mainly on bluegrass and tall fescue.
The next moth is a Lucerne Moth (Nomophila nearctica). This is a common species that I have posted here before. This individual is more darkly marked than the one I found at Davidson Mill Pond Park.
The next moth is a Changeable Grass-veneer (Fissicrambus mutabilis). These moths are found in lawns and other grassy places; their larvae feed on grasses. Above you can get a close look at the mouthparts (palps) that form its snout.
This is the same moth perched on the side of an empty film container that I use for collecting specimens. I refrigerate any that I capture and then release them once I have photographed them. This angle gives a better view of the key markings, the post median and subterminal lines. The photo also shows a characteristic posture of grass-veneer moths; often they sit with their heads angled down and the tips of their wings angled up. I am not sure if this provides better camouflage or if it helps the moth take flight faster.
I think that this last moth may also be a Changeable Grass-veneer, though it lacks evidence of a subterminal line. The other related species do not fit quite as well.