I've been wondering about the settings used for "Save As (.png)" option available in Photoshop. Does it save the highest quality, largest size as a default setting and how does it differ from PNG-24 and PNG-8 in "Save for Web"? Let me know if I can be more detailed in my question.
Not really. Save for web let's you save multiple files at once. Let's say you have a web page. You can slice it and choose a different format and settings for each slice. Also you can see a comparison between jpg, gif, png and decide what format gives good quality and small file size for this slice. Sometimes size is drastically different while quality is almost the same. I always save with Save for web, because I see a preview.
.png images are mainly used to save images with transparent backgrounds. ex-logos.
Save for web advantage - We can choose lower file size without much quality difference from the original. The difference in quality can be viewed in the preview. It is good for websites, as lower file size takes less time to load. Png -8 has less size and low resolution, on the other hand png-24 has more size with high resolution. But these two formats are of less size than normal png file.
Hope it helps.