I had a day stay at the Sheraton Heathrow a month ago. To me it was pretty obvious what the Day Stay Rate was for - checking in and out the same day.
What was not clear in any way was if there was some restriction on the hours it was available. As a previous poster has said checking in and out on the same day could mean in at 1am out at 11pm. Whenever I have seen day use rates before there has usually been some restriction like "Check-in after 10am, Check-out by 6pm" This of course reflects the whole point of Day Use Only rates which are common at airport hotels but not elsewhere - many people staying overnight at airport hotels are flying out early the following morning and many don't arrive to occupy their room for the next night until late that evening. So a large number of rooms are vacant through the day and a 10am to 6pm restriction makes sense.
My criticism of the SPG website is that it doesn't give you any idea of these restrictions when booking the rate. As it was, an Endless Weekend Rate for only 5 pounds more was available and as I was arriving at 8am and leaving at 7pm I decided to book the overnight rate and hope for an early check-in rather than risk arriving at 8am and finding out that the Day Use rate was only valid for a very restricted number of hours.
Bottom line - if SPG is going to put the rate online, there needs to be better disclosure of terms but I would never have expected to have been able to arrive at night and stay till the next morning on a Day Rate.