Hard to tell specifics on these without being there. First is some sort of holly, second a privet. Hard to tell what kind of privet, but likely glossy privet. Pinch a leaf and hold up to light and if there is a halo around leaf, then glossy. Regardless of variety or species, both are common and pedestrian hedges.

Dan

The first looks like Dwarf Burford holly. The second looks like Ligustrum japonicum. Both are rugged, tough shrubs and can take whatever heat Texas can dish out. Yes they are pedestrian, but with a bit of pruning can look good year-round.

Dave in nova is calling them the same things I would.

Thanks for the ID help. Should I be worried about the yellowing on some of the internal leaves of the Ligustrum? Some areas are much more yellow than these particular photos show.