I like to think of thread synchronization as a bottom up where processor and operating system provide construct that are primitive to more sophisticated
At the processor level you have CAS and LL/SC which allow you to perform a test and store in a single atomic operation ... you also have other processor constructs that allow you to disable and enable interrupt (however they are considered dangerous ... under certain circumstances you have no other option but to use them)
operating system provides the ability to context switch between tasks which can happen every time a thread has used its time slice ... or it can happen due to otgher reasons (I will come to that)
then there are higher level constructs like mutexes which uses these primitive mechanisms provided by processor (think spinning mutex) ... which will continuously wait for the condition to become true and checks for that condition atomically
then these spinning mutex can use the functionality provided by OS (context switch and system calls like yield which relinquishes the control to another thread) and gives us mutexes
these constructs are further utilized by higher level constructs like conditional variables (which can keep track of how many threads are waiting for the mutex and which thread to allow first when the mutex becomes available)
These constructs than can be further used to provide more sophisticated synchronization constructs ... example : semaphores etc