I received the first picture from Rob Elder of Omaha Organics. It is a stolon of bermudagrass Cynodon dactylon. As is the case in central Iowa, this is unusual for the Omaha area. Not long ago, you would not have found this species in that area because it would die each winter due to the cold weather. It is now surviving the winter.
How can you tell it is bermudagrass? While the long stolon is a pretty good clue, there are other species with stolons, so you have to look close at its characteristics. The first clue is vernation, as pictured below. Vernation is the way in which new blades emerge from the sheath. Bermuda is folded like the grass on the left, while Zoysiagrass is rolled like the grass on the right. Creeping bentgrass can also form a stolon like the one above.
Bermudagrass and Zoysia have a hairy ligule like the one on the right in the picture below, whereas bentgrass has a membranous ligule like the one on the left.
Here are two actual pictures of the hairy ligule of bermudagrass. If the grass that you are trying to identify has a membranous ligule, it will likely be a cool-season grass. If it is a warm-season grass like bermuda or zoysia, it will have a ligule that is a fringe of hairs.