Generally speaking, all police in Texas are equal. Various state police (TABC, DPS, TPWD Game Wardens, etc.), city police, city fire department arson investigators, county police (sheriff, DA investigators, constables, etc.) and others are all under the classification of peace officers. Most laws do not distinguish which laws they can enforce or on or off duty and in sone cases, active duty or retired. There are some specific authorities in very limited situations where authority rests with certain agencies but for probably 98% of the time an officer is an officer. One example is that officers have authority to make arrests statewide but traffic jurisdiction only in their county.
Texas police have no authority to enforce laws outside of Texas unless that state grants cituzen arrests OR the officer has been granted that authority by an agency in that state, like being deputized. I have been a Missouri police officer for about a week each year for over 20 years as an example.