This first is Lycoris squamigera, the most common one around here. There is even a guy at our farmer's market who sells the bulbs. Ours were here before we were, so we assume they were Mrs. Rhoric's like the old daffodils, though they might pre-date her time here in the 40s. Not likely they were planted after that since the place was a rental or empty for a number of years until Hank bought it in the early 70s. Obviously they are long lived and form nice sized clump over the years. You see them everywhere this time of year, all over the county, all seeming to have come up on the same day.
The second one we grow is newer to us. We tried it a few years ago, but the place where it was living got too shady and it disappeared. We got 5 bulbs this spring from Brent and Becky's Bulbs and 4 of them have bloomed, despite this mini-drought we're having. The color changes day by day and varies between pinks, blues and lavenders, sometimes all of them on the same flower. Quite unusual. They seem to be a bit smaller than the pink ones above and a bit more delicate.
Fot those in warmer climates, there are also ones with red, yellow or white flowers, probably more, but they are mostly for zones 8 to 10, places where it is just too hot for me.