Possibly cotoneaster?

I suspect that there are two different plants being shown there.

The fruiting plant sure looks like Ilex decidua, which is a TX native. I don't recognize the other.

I vote that more closeup images be provided when requesting ID of unknowns. Many plants can be ID'd from buds, stems, bark, leaf scars, fruit, lenticels, stipules, etc. - but not if they cannot be seen.

I agree. The berries are borne on almost naked deciduous stems. They do not go with the evergreen leaves. For future reference honeysuckles have opposite leaves.

If there are opposite leaves shown ( I can't tell) then they probably belong to Privet (Ligustrum sp.) In Texas.

Ah yes, so it does turn out that the big leaves were from an invasive Glossy Privet crowding through it...

As I went back and got some better pictures and confirmed that yes, it is a native Possumhaw (Ilex decidua)!

Really lovely pop of color coming into Winter...along with American Persimmon leaves!