Many states do it different ways.
Those which do not have a daily entrance fee tend to have higher daily camping fees.
For a short trip as you mention - paying the fee might be cheaper than buying the annual pass. Note that with the annual pass you receive half off the camping fee for one night on up to four different two night (or longer) camping stays each year.
Note - not all TX State Parks charge $7. Monahans Sandhills just off I-20 west of Midland/Odessa charges $3, Lake Colorado City is $4, Abilene SP is $5 - so if traveling across Texas on I-20 - you can use the cheaper fee parks.
Research the individual park on the Texas State Parks website.
The process is that when you stop at the park entrance station - you either pay the entrance fee, or you show the park pass. Then you get a receipt to be displayed on the vehicle windshield.