I have a Samsung galaxy watch 5 pro running the latest version of WearOS 3 I want to build an app that use the watch sensors and send the reading into android smartphone
there are the WearOS android SKD which is closer to android developer and there is Samsung Privileged Health SDK what is the difference between them
Yes, you can obviously develop apps for Wear OS. As for Samsung Privileged SDK: it is compatible both with Wear OS and Galaxy Watch (4 and above according to their website).
The difference is in API itself. While it might be similar in functionality you will see differences. Please, refer to the official documentation as it is too much broad question.