Like others have said, it's almost certainly a DoF issue. You're probably seeing a difference because of the much larger sensor in a DSLR versus a digital PnS. The PnS's tiny sensor means that DoF effect is minimized to a large degree, so it's more common to have more things in focus at once. The problem is that you can't get great shallow DoF when you
want to!
As for Hyperfocal... this is on where it helps a lot to have an older and/or high-end lens that actually has DoF markings on it. The reason to use the hyperfocal distance actually directly related to Dcanoli's question.
Think of it this way. At a given aperture, you'll have a certainly size DoF. If you set your lens to focus at infinity, then you only get about half of your available DoF - in other words, you'll get the range of things closer in focus, but since you're already at infinity, the extra DoF is effectively "lost".
In order to get the maximum DoF, you need to focus at the hyperfocal distance - this is the focus point where, as your given aperture, infinity is just barely in focus. This will give you the largest possible DoF while still keeping far-away objects sharp and in focus.
Now, ideally, you are using a lens with the markings that tell you this information... for example, here's my Zenitar 16mm fisheye (I just happen to have a decent shot of its markings online.)
The red line in the middle is where the center of your focus is. The yellow markings above it are the distance, this is part of the focus ring. This is currently set to focus at about 1.2 meters. Now, notice the matching green aperture numbers that are on either side of the red focus indicator. Those tell you the DoF for that aperture.
To get the hyperfocal, you move the infinity indicator to the marker for the aperture you're using. In this shot, if you're using F8, you should be able to get infinity in focus. Looking on the other side, F8 likes up to around 0.65 or 0.7 meters. That means that at the current focus setting and F8, everything about from 0.7 meters to infinity will be in focus. This is a pretty huge DoF, because it's such a wide lens - set it here and by and large, you don't even have to worry about focusing it, because virtually everything will be in focus. For comparison, if you focused the lens directly at infinity, your DoF would only be around 1.2 meters to infinity - the difference would be quite a bit more on a lens with more focal length.
So, are you thoroughly confused yet?

Obviously, hyperfocal is much easier to determine when your lens has all the markings, which is getting rarer and rarer nowadays. Even rarer is the little red "R" that's on that lens, that is for infrared photography.