A window hinged at the side is called a casement window.
More specifically, that is a slide hinge, manual, sector crank casement window.
Different manufacturers may have a different name for the 'slide hinge' style. Its purpose is to allow easy cleaning of the outside of the pane.
It's 'manual' because you turn the crank by hand. Some industrial buildings have motorized window cranks.
I'll take your word for it that it has a worm drive. Mine have little pinion gears. If the mechanism includes a member that looks like a partial gear wheel attached to a lever, that's a 'sector crank'.
If you're searching or shopping for this kind of window, don't bother with the 'worm drive' and 'sector crank' terms as these vary with manufacturer choice. Use the terms 'casement' and 'slide hinge' to find these kinds of windows.