I have recently noticed (mostly because I have turned on Strict HTTPS in my browser so that it does not allow mixed content on HTTPS pages) that when one uploads an image to a question or answer using the standard in-built functionality which uploads it to imgur and puts it in this format:
[![enter image description here]] : http://i.stack.imgur.com/YqVpb.png
It makes it display it to you using HTTP rather than using HTTPS which is available. Now however in chat the same in-built upload functionality uploads it to imgur and then shows it to you through HTTPS as the same image would be uploaded and then displayed as:
So I think that for security and consistency reasons they should both show the images through HTTPS so that when one uploads an image to a question or answer it displays it through an HTTPS connection as it does for uploaded images in chat.