European Lily of the Valley, May Bells, Our Lady's Tears, are all names for the same plant, Convallaria majalis.
It grows from Zome 4 to zone 8. All parts of the plant are poisonous if ingested.
Attractive to bees, butterflies.
Invasive, can become a noxious weed in certain situations.

White coral bells belong to Heuchera
The cultivar Silver Scrolls has white to near-white flowers.
Cultivars of Heuchera sanguinea have flowers that may be white, pink, or shades in between. Heuchera pubescens is always white to near-white.
Also attractive to bees.