72 DPI or 300 DPI - Which Is Better For Web And Print Both?

For web, you can work at whatever size (dpi) you're comfortable with. It doesn't make a jot of difference whether you work at 72dpi or 720 dpi as you are working to physical pixel DIMENSIONS as opposed to have to work with RESOLUTION constraints. One thing to bear in mind, though, is that if you create an image in Photoshop on a 'normal' ~72 pixel per inch screen, seeing it on a Retina screen at a far higher ~200ppi, your image in Photoshop is going to look a lot smaller at normal size, even through the physical size is exactly the same.

For print, however, it's an utterly different ballgame. It's OK to be asked for a 300dpi photo (bitmap image) but you need to know how it will be used. For vector artwork, this isn't an issue. For instance, the minimum requirement for a screen-printed magazine ad and that of a 96-sheet billboard poster are majorly different. The magazine will typically ask for a 300dpi image which is *about* right. However, for your billboard poster, that number is closer to 30. If you are looking at something close up, in order for the image to be crystal clear, the dots (or pixels in the on-screen sense) need to be close together. For items you look at from afar, that is not the case. In terms of file size alone, a 300dpi 96-sheet poster would be HUGE!! Knowing that in itself could save you from major headaches...

As usual Test Screen Name has come up with the succinct and excellent answer – building on his elephant metaphor, it's horses for courses. Most people seem to build websites nowadays that are around 1000px wide so no image should be wider than this, often smaller, but you can add links on your site to hi-res JPG images and PDFs that users can download for printing themselves.

And bear in mind most people are viewing website on tablets and smartphones phones, so your site should be designed to be responsive (rearrange itself to suit the viewing device).

Pixels are screen units. That's what you go by when designing for screen.

Dpi is a print term and has no relation to the screen pixels.  The more accurate term is "Pixels per Inch" It's actually instructions to the printer.

A 100 x 100 px image will cover one inch of paper when printed at 100 ppi.  Increase print resolution to 300 ppi and it will be about 1/3 x 1/3 of an inch.

72 ppi is a legacy term from the old 1984 MacIntosh screens. If there is no print data, that's what Photoshop defaults to.