I think a screencap is when あなた just take whatever is on the screen and make it into a picture. I mean like for a screencap you'll literally take your camera and snap a pic of the screen, または you'll hit ALT+PrtScn to make a キャップ of your computer screen. Plus, screencaps are of the entire screen, normally. No cropping または whatever.
I think 写真 are もっと見る edited and planned, rather than a ランダム pic of a ランダム scene.