The Sandia Mountains include three species of oak, which hybridize, and a fourth named "species" which is one of the hybrids. Each of those named oaks is shown below. In deciding which name to use, don't go by a few leaves; instead, see what leaf form is dominant on the plant as a whole.
Plants are organized alphabetically by genus and species. Hover over a photo series to control the images.
Gambel Oak (Quercus gambelii)
The hallmark of this species is the large, deeply lobed leaves. Gambel Oak grows as a shrub when colonizing burned or otherwise disturbed patches of forest. Given enough time, water, and competition for sunlight, it becomes a full-sized tree. In the fall the leaves may turn a fiery red, due to a sudden sharp frost, or they may just fade to brown.
Gray Oak (Quercus grisea)
Look for small, stiff leaves that are oval with pointed ends. Also, the shrub or tree will be dominated by leaves whose sides don't have pointed teeth.
Shrub Live Oak (Quercus turbinella)
Look for small, stiff leaves that have pointed ends. Also, the plant will be dominated by leaves with pointed teeth along the sides. The word "dominated" is important. In my photo showing the acorns, the adjacent leaves don't have many side teeth, but most of the leaves on that bush had classic Q. turbinella leaves.
For decades I referred to this species as scrub oak, and that's one of the common names, but folks in the Southwest often refer to any shrub-sized oak as scrub oak.
I don't know of a name for Q. grisea-turbinella hybrids.
Wavy-Leaf Oak (Quercus X undulata)
The X in this plant's Latin name indicates a hybrid (cross). The botanical checklist for the Sandia Mountains remarks, "This hybrid between Q. gambelii and Q. turbinella or Q. grisea is a dominant form of shrubby oak in many relatively dry habitats." As the common name suggests, look for a wavy edge. As far as I can tell, Quercus X pauciloba is a synonym.