I would guess you are on Mac. Because with the 'save as...' there is some additional information included in the file (resource forks or tasty sounding stuff like that), that can be discarded in a lot of processes. Like showing stuff on the internet or using it as texture maps. In the 'Save for web' way of making jpg's, the small file size is the most important, so every unneeded bit it left out. And the file will always be rgb, for instance. So there difference in file size is not connected to quality, when you use the same setting. I always use the 'save for web'. But for textures I mostly use .psd or tif files.