Conservative Jews (less observant that Orthodox) and Reform Jews (less observant than Conservative) are less restrictive. So, for example, Orthodox Jews may refrain from work the entire holiday, but Conservative Jews just the first day or two.
I assume the website can stay up since as long as it's not taking orders it's passive. I would guess that if there was a problem with the website, repairs would not start until after Sabbath.
Perhaps more than you wanted to know.