I've been riding with an 80 stem on my C'dale for 14 years. It's about time I stretched out like I should, so I ordered a 110 stem. The diameters match (bars and head tube), but the styles are different. The old stem has a circular disk inside the stem that tightens inside the head tube - I think I might have seen these called "quill" style? The new stem is the kind I'm familiar with - the wedge shaped piece tightens against the inside of the head tube.
My question is whether these styles of stems are interchangeable. Will I damage my frame if I use the new style stem?
Both stems "wedge" inside the headtube when tightened. You can use either type in your bike.
It does look like you have some rust in your head tube. Perhaps you should get your headset checked out and make sure the bearings are OK. Make sure you grease the wedge and quill before you put your new stem on the bike.
For what it's worth, the stem binder bolt doesn't have to be tight enough to hold the whole bike together. If you overtighten it, it can form a bulge in the steerer tube on your fork. That's a bad thing. 15 to 20 ft/lbs is the torque spec. for stem binder bolts. After tightening, if you hold the front wheel between youd knees, you should be able to turn the stem and handlebar assembly.