This type of fittings is so unique that it could be considered a special - but according to generally accepted classification it belongs to a separate category with a name. Hardly a defining feature of these handles is the necessity of installation without cutting in - glass is fragile, you'd better not try to treat it mechanically too much. A handle that fits your needs, without any drilling, is a value in itself: it does not take long to install, and it is easy to use.
As you can see, handles not only differ in shape - there are different ways of opening, types of fasteners, and especially many variants of materials. Popular varieties: staples, knobs, lever models, stationary, coupe (mortise). For example, push handles for glass doors are not the most common, but universal - suitable for wooden, metal hinged-type leaves. There are with a lock or with a thumbturn.
The most suitable handle for the glass door without drilling
As practice shows, it is possible to fit any model - otherwise it is better to choose with a caliper and the door in the hands. Of the above types, the most quotable are staples - you can put them on almost any sash.