Weird scenario: Different File sizes in same jpg

[remake]

Few years ago I have been presented with the following scenario which I tested and to my amazement I couldn't explain it back then. Nowadays I know it can't be true as I started to study JPG compression and the JPG file size is in no way associated with it's extension.

The scenario. My friend comes and says: You won't believe me. Save this image as .log.jpg instead of only .jpg and you will get a smaller file size under the same compression. I thought this was the most stupid thing I heard all day. Well, somehow he was right. Arguably I think now the file saving was done in Paint not Photoshop and there you can't set your compression like in Photoshop.

I bet everyone will now agree with my opinion. Paint was probably offering different compression, but the question is why?

Also, if someone can test this in Photoshop too it will be awesome. I don't have it installed on my laptop right now.

[aartist]

Paint Shop allows different compression JPG saves.

[Quantum3]

if a normal Jpeg and that one you mention have dofferent sizes in KB then that's.