Whether to choose a wrist brace, wrist support or a wrist splint depends on your injury or condition and how much it's already healed. Generally, the more severe the wrist is affected, the more support it needs. After surgery, complete immobilisation is needed for the wrists to heal in the right position, so a brace with splints is the right choice. Has the bone healed completely or at least mostly, wrist supports without metal splints can help to deal with the remaining symptoms like pain and swelling, but compression also helps the scar tissue to heal since it improves circulation.
Minor injuries often don't need to be immobilised completely, stabilisation from the compression is enough for the tendons and muscles to recover. The tight-fittings wrist wraps apply constant gentle pressure and keep the area warm. For some injuries, cold therapy is advised. In those cases you should use a brace without compression. It will keep the wrist stabilized and offer space in between the splints to apply cold compresses or cooling gels. Which support or brace is right for your wrist condition should always be determined by a doctor.