What do you call conventional wood staining that doesn't result in a glazed effect?
I'm not sure there is a term that exists for cabinets without glaze. As you mention, this effect is really popular right now, and it's going to be difficult to find non-glazed cabinets from a big box retailer.

You could try working with a dedicated cabinetmaker and express your interest in some non-glazed examples.

To others who are confused by the question. Glaze is not a stain. After a stain is sealed, a glaze can be added (to add highlights, shadows), which is then sealed again under the finish of choice (e.g. polyurethane).

One can buy glaze, or they can make their own by mixing acrylic paints (the dye) and some sort extender (e.g. paint thinner and linseed oil, or clear acrylic glazing liquid).