The sensor size is different among DSLRs and compared to 35mm cameras. In the case of Nikon, there are 2 sizes. One is the "FX" which has about a 1.5 ratio for focal length... in other words, a 50mm lens on an "FX" camera behaves like a 75mm lens would on a 35mm camera. The Nikon "DX" (expensive!) has a sensor that is similar to a 35mm film "footprint" so a 50mm lens on a "DX" camera behaves like a 50mm lens on a 35mm camera. Canon chose to complicate things even more by having 3 different sensor sizes on their DSLRs. Their low-ish end DSLR has a 1.6 ratio and it goes up from there to a "35mm like" sensor.
The apertures are the apertures.
The smaller sensor cameras can get by with "less glass" in the lens because a smaller diameter is needed to "cover" the sensor which makes them lighter, cheaper and smaller. The lenses made for 35mm cameras or large sensor cameras are backward compatible to small sensor cameras but you may not want to use them because the lenses are larger, heavier and more expensive. A "DX" lens would not work well on a 35mm camera or "FX" camera as the corners would be "shaded" (dark).
For my purposes, the "FX" is fine as would be the Canon 1.6 sensor. When you can make a 20"x30" print of something without any bad evidence of your sensor size, I call that good enough. I shot weddings for years using both 35mm and medium format (6x6). For ALL the prints ever I made, 35mm would have been adequate. The dirty little secret in the industry was that if you used medium format, you could charge more for weddings. To me, the "FX" vs. "DX" sensor is a similar story. One more thing on sensors... Camera manufacturers are getting better results "per square centimeter" with their sensors more recently. An "FX" (1.5) sensor from a Nikon D40/D50/D70 does not deliver the quality as the new "FX" (1.5) sensors you might find on a D300/D300s/D7000.
It is important to be happy with your gear but it is every bit as important to really understand what attributes in your gear are truly important. If quality of photograph is REALLY REALLY what you want, spend $250 on a used Mamiya 645 (they're on Craigslist all the time and that price is often with 2 lenses) and shoot 120 film. Spend $7000 on digital gear and you won't achieve the quality of the Mamiya. Admittedly, the new gear has fantastic electronics and features but those things don't do much for the quality of the photograph. Disclaimer: I have a Nikon D7000 and I love all the bells and whistles.
Point and shoot cameras have smaller sensors than the "1.6" or "1.5" sensors with understandably different operating parameters and expectations. There are currently only one or two exceptions. When you read that a point and shoot is 12 megapixels, does that mean that it will have better quality than a Nikon D40 which has 6.1 megapixels? The D40 will deliver much higher quality pictures because it has a larger sensor. This is a whole different conversation but understand that pixel count is less meaningful than sensor size (and quality).
