Hmmm... now you made me go fetch my iLiad, turn it on and look at the icons, LOL.
There are four icons on the left in total, the first (on my iLiad) looks like a mix between your friend's and yours, it's a small dotted rectangle on the bottom left with a diagonal arrow to a large solid line rectangle, the second is a small solid rectangle with four arrows going to a larger dotted rectangle (to go to "fit page" zoom, so it does nothing but refresh if you haven't zoomed), the third is the pan option (disabled until you zoom) and the fourth is the landscape/portrait icon.