In the Epson driver, you're not giving the print size, rather you're choosing the size of the physical paper that you've loaded into the printer. In Photoshop's print window, you're then choosing the size of the image to print on the paper. The two sizes don't have to be the same, and indeed if you leave a blank margin around the image to make it easier to mount & matte the print, then the print size (in Photoshop) would always be smaller than the paper size (in the driver).
For your specific example, if you wanted to make a 16x20 print, in many cases you'd probably be using cut sheets that come in 17x22 size. So in the Epson driver, you'd pick 17x22. Then in Photoshop's print window you'd enter 16x20. Of course, you have to watch out for aspect ratio. You can't print a 16x20 (4x5 aspect ratio) of an uncropped Nikon shot, because Nikon images have a 3x2 aspect ratio, not 4x5. So you'd first need to crop your image to the aspect ratio that fits how you want to print the image; or choose a print size that is scaled up from the "native" 3x2 aspect ratio, in this example perhaps 14x21 rather than 16x20.
This also involves DPI (actually PPI -- pixels per inch) as Jim describes. Epson printers typically expect images to come in using 360 or 720 PPI, so if you're resizing and/or cropping images yourself, you need to be aware how pixels and inches are going to convert. (Digital image files are measured only in pixels, inches aren't relevant until you're going to print on paper at a given size of inches. Then you need to know how many pixels will be laid down in one inch of print.)
There are many additional details of course.
E.g. you bring up the question of changing image size in the Edit > Image Size menu item. You don't need to, because you can set the size in the print window and Photoshop will scale the image pixels up or down as required to match the size in inches that you give it. But there are reasons why you might want to do the scaling yourself by changing the image size. Mainly this would be to interpolate the image to the resolution the printer driver will be expecting, in order to perform a final pass of output-size-dependent sharpening on the image before sending it to the printer.
Then there's a bunch of stuff around color management: how to choose printer profiles, and configure Photoshop and the Epson driver to make sure color will be rendered properly. This in turn can drag in the topic of soft proofing, to simulate how your image might look given the color management process that will be applied to it, but doing so on-screen before you print so you can potentially adjust things before wasting paper. This in its turn drags in monitor profiling, since a common complaint is "the prints are too dark!" when the real problem is "the monitor is too bright".
Etc.
A good starting point to survey the topic of printing is Eric Chan's pair of printing articles:
http://www.naturescapes.net/docs/index. ... t-printing
http://www.naturescapes.net/docs/index. ... ter-prints