Recognizability between mobile and desktop

How much can a design change when adapting it for mobile? I go by this rule: the mobile and desktop versions should be mutually recognizable. If I’ve used a website on my computer and then open it on my phone, everything should be where I expect it to be — and vice versa. If, say, there’s a row of six images on desktop and on mobile it becomes two rows of three — that’s fine. But if the images are…