Most likely your relative position on the server has changed. "/images/image.jpg" points to "http://server.com/images/image.jpg" but "image/image.jpg" points to "http://server.com/currentpath/image/image.jpg".
Generally if you use forward slash ( / ) operator it will search and include the given files from root directory .But if you use without ( / ) then it will include files by searching from current location.
So in your issue
<img src="images/image.jpg"> it had searched image.jpg from current directory then images dir --> in that image.jpg -->found and hence worked fine .
But in other case it start to found from root....not found and hence no result