These are different varieties of Phlox subulata or moss phlox. They typically come with bloom colors ranging from white, light pink, purple, to more of a magenta red color like the first photo. 

They prefer full sun and well draining soil. They bloom in spring but the foliage stays green through the winter. Sometimes you can see them in wild areas growing between rock crevices. 

They are a nice native and tough perennial to add to your garden! 

Emily

You read through our resource page on Checkweed. There are a few different species but most are cool season annuals so it will fade when the weather heats up. You should try to hand pull most of it before it goes to seed. You will likely have some that will return either in the fall or next spring and you will just have to pull those as well.