If there is an opening but no (or a short) covering sheath for each finger they are called fingerless gloves. Fingerless gloves having one large opening rather than individual openings for each finger are sometimes called gauntlets, though gauntlets are not necessarily fingerless.
Gloves which cover the entire hand or fist but do not have separate finger openings or sheaths are called mittens. Mittens are warmer than other styles of gloves made of the same material because fingers maintain their warmth better when they are in contact with each other; reduced surface area reduces heat loss.
A hybrid of glove and mitten contains open-ended sheaths for the four fingers (as in a fingerless glove, but not the thumb) and an additional compartment encapsulating the four fingers. This compartment can be lifted off the fingers and folded back to allow the individual fingers ease of movement and access while the hand remains covered. The usual design is for the mitten cavity to be stitched onto the back of the fingerless glove only, allowing it to be flipped over (normally held back by Velcro or a button) to transform the garment from a mitten to a glove. These hybrids are called convertible mittens or glittens, a combination of “glove” and “mittens”.