An adversarial GM runs the game as if the players and/or their characters are the enemies.
But how much of it is adversarial vs a misalignment of expectations?
Probably half of it. I try to do my best to run the game knowing all of my NPCs are expendable and the PCs are not. However, when I invest hours writing story arcs and plots, designing encounters and dungeons, and then all of it falls apart to crappy dice roles it's really easy to get upset. It's also difficult to fight off the instincts to fudge the numbers and have it play out in a way that best suits your original vision. That's not adversarial, it's just not GMing.
A big part of being a GM is letting the players be story tellers, and have their PCs lead the story in a direction they want. Sometimes it's hard to let go of your original plans and go in this new direction, which is what makes dungeons great for GMs as they confine the story to a known section of the world. And this is where the difference can really stand out. A normal GM tailors a dungeon to challenge their PCs, thus letting them engage in a story from a point of weakness with the knowledge that they can and should win, albeit a costly victory. The adversarial GM will change the rules to punish players, force PCs to lose, and ensure that even in strength their victory is costly. The PCs are handily winning? More monsters show up! Now the PCs lose. There's an unusual situation that might benefit the players? Not this time. It comes up again later? Well, it benefits the NPCs so the ruling is applied differently now.
Let's be honest here, the GM can beat any party because their resources are unlimited. Only the players and their characters are limited. They have level limits, experience limits, action limits, everything they have is reigned in to ensure all of the players and their characters can participate, and none of them completely overshadow the others. The GM has a completely different role. It's to design a campaign that challenges the players and their characters, showcasing and outlining their strengths and weaknesses. The story is told together, as a group. Cooperation is key. If there's no sense of cooperation then someone, GM or player, is being the adversary. That doesn't mean there's zero competition. Not at all. There's lots of it, but always in the spirit of the game which is a cooperative story.