If I thought about it I would be surprised to NOT see charcoal grills in the picnic area of public parks. The four I frequent with the kids (Memorial, Herman, Hedwick, and Bear Creak) all have them and Hedwick is an itty bitty park with just a playground area (the others have sports fields/public monuments Bear Creek has an animal display. Herman Park has The Zoo, Miller Outdoor Theater, Houston Museum of Natural Science, Memorial is a monument to WWI soldiers (was a WWI camp) multiple tails, fitness center, pool, and the Nature Center)
The thought is these are safer than people bringing their own portable ones and dumping out still hot coals to go home. (Portable grills are allowed but have had some restrictions due to the drought and the fact the parks have been basically tinderboxes. Memorial lost so so many trees. Paying for natural gas or propane - that isn't going to happen. Setting up BBQ - by Texas standards is also not going to happen. Occasionally I see people having moved a real BBQ into Bear Creek.
Portable Grill for grilling things like hot dogs, hamburgers, chicken
BBQ grill for smoking meat for hour - in Texas usually brisket
I still remember visiting PEI and being invited over to my aunt's house for a BBQ. Seeing no sign of a smoker and whispering to my Daddy that we were going to starve before the meat was ready. (My parents would have started the Brisket at 6 am for a late lunch early dinner), and Daddy explaining that Aunt had invited us over for hamburgers and hot dogs. I was still concerned because no fire had been lit so it could burn down - they all used gas grills something none of my family in Texas would use at that time (King of the Hill might be accurate for Dallas but not Houston)