We call it Swamp Sunflower out here. Grows in the ditches and wild places. Continues to grow from the roots as well as drop seeds. Hardy. Perennial. Comes back faithfully. Can be cut back so that it stays lower to the ground if you only want flowers 18" high for example. Single stems easy to pull out if you want it thinned or have stragglers you don't want. Flowers are long blooming and look nice. Repeat bloomer especially if you deadhead. Heidi

It is easy to know if it is mugwort as previously stated above by two of us. Not complicated at all. Artemisia leaves have a silver reverse. https://nakazora.files.wordpress.com/2012/05/yomogi_underside.jpg And yes, check for the silver undersides.

Thank you. Pycnanthemum virginianum seems to be a good match for the first plant. I'll go back this weekend to see if the second one is blooming. That might make it easier to identify.

Callicarpa for the shrub. I would recommend posting id questions on the Name the Plant Forum where there's a wider audience of people specifically interested in identification. https://www.gardenweb.com/discussions/namegal