dr_snapid's comment that "the server sends every Nth line" is not entirely true. A web server need not know anything about the contents of the file it is sending; its job is simply to send the data. Rather, the image is created in such a way that the data corresponding to "every Nth line" appears at the beginning of the file, with the details becoming able to be filled in as more of the file is received by the browser. In PHP's case, the data may have been generated dynamically instead of pulled from a file, but this does not change the fact that it is the data itself that is different, not the manner in which it is sent.*
In fact, with JPEG, it is less "every Nth line", and more "every Nth pixel", where N is gradually decreased, resulting in a grid that gets progressively more fine-grained as the data is received (hence the appearance of a low res image becoming more detailed). The browser basically estimates what goes in the gaps between pixels, probably by simply blending between the colours, whilst the "real" data continues arriving. This is a fundamentally different method for encoding the data when compared to non-progressive JPEGs, and coupled with the format's other compression techniques, may indeed result in a different file size.
*Can you imagine how much more buggy the Web would be if servers were expected to send different file types using different algorithms, and browsers were expected to be able to receive every one of them?