We don't capture images on a daily basis - in fact, you can choose any dates in the future or any dates in the past!
Our star catalogue comes from the European Space Agency's Hipparcos mission, a high precision catalogue of stars generated from over three year's of observations by the Hipparcos space-based telescope. You can read more about it here: https://www.cosmos.esa.int/web/hipparcos/home
The maps render stars all the way down to magnitude six (visible stars, under dark skies). If you follow the links to the create/edit page, you can see the maps updating as you make adjustments. If you click the "Save your design" link, a digital copy will be emailed to you for closer review.
At our scale, the positions of stars relative to each other and our solar system change very slowly. The constellations look the same as when the ancient Greeks named them hundreds of years ago, and they will look the same hundreds of years from now.
However, the stars that are above us each night do change through each night, season and year, because as the earth rotates and as it tilts moves around the sun through the seasons, it changes the parts of the sky we are looking at above us, from Earth.
Astronomers have carefully studied and measured the positions of the stars and the year-long orbit of the earth around the sun and so, using math and (yay!) science, it is possible to compute what stars will be above anywhere on the earth at any time! We use a catalogue of star locations from the Hipparcos satellite and these computations to generate our Star Map unique to your chosen location and time.
One last little fact: The stars we see each evening change with the seasons in a yearly cycle. The stars you see on your birthday or special anniversary will be the same each year. So, even if your Star Map is for a date 40 years ago, you can still go outside on the evening of that date, this year, or for years to come, and you will see those same stars above you!
Hope this helps!