A hybrid mutex behaves like a spinlock at first on a multi-core system. If a thread cannot lock the mutex, it won't be put to sleep immediately, since the mutex might get unlocked pretty soon, so instead the mutex will first behave exactly like a spinlock. Only if the lock has still not been obtained after a certain amount of time (or retries or any other measuring factor), the thread is really put to sleep. If the same system runs on a system with only a single core, the mutex will not spinlock, though, as, see above, that would not be beneficial.
A hybrid spinlock behaves like a normal spinlock at first, but to avoid wasting too much CPU time, it may have a back-off strategy. It will usually not put the thread to sleep (since you don't want that to happen when using a spinlock), but it may decide to stop the thread (either immediately or after a certain amount of time) and allow another thread to run, thus increasing chances that the spinlock is unlocked (a pure thread switch is usually less expensive than one that involves putting a thread to sleep and waking it up again later on, though not by far).