Far from basic point-and-shoot cameras (though there are certainly models that do just this) the more reputable trail camera manufacturers offer devices that come in all shapes and sizes. Making a conscious decision about which features you'll need and others you can live without will stand users in good stead for purchasing the right device. Still image and video resolution (including video frame rate) is important, but so too is cellular connectivity so that you can view or record from remote locations. Good night sight or a dedicated night-time image sensor is essential for capturing subjects in the dark, but some cameras come with an undetectable infrared option, too.
If visiting the location is difficult or likely to disturb shy subjects then solar panels can help prevent the need for battery changes, as they sport rechargeable lithium ions. Strong camouflage or plain earth tones also help trail cameras go undetected by wildlife subjects and security threats if using the camera for this purpose.
Composition can be tricky when setting up a wildlife camera, so if that's important then consider a unit with an LCD built-in so that you can line up the device before leaving the area. Weather sealing and durable construction are also important, as are operation temperature ranges if you're planning on using it somewhere extreme.