I found lots of examples for 'landing card' when I did a Google Search, but didn't find any examples of the newer ones that ask how long you're staying, but I think historyenne's got it right. They really don't ask for a lot of information.
Anyway, do a Google Search for 'UK landing card', and you'll be able to see lots of photos of what they look like...don't know if they've changed much, since I haven't traveled since they now ask how long you're staying...