If you use multi-threads to do something at the same time, that is a Synchronization.
You need to control threads to avoid Race Condition and Critical Section.
mutex and semaphore can solve the critical section.
But what’s different?

Mutex is an object and binary semaphore .

A semaphore is a signal, and a thread that is waiting on a semaphore can be signaled by another thread (more then 2 threads).
But you should notice that the wait and signal operations require to be executed in the correct order. Nevertheless, deadlocks will occur in semaphore.

Roughly, a mutex would be referred to as binary semaphore.
There are many dufferences, you may refer to this website.
https://www.guru99.com/mutex-vs-semaphore.html

How can we use semaphore?

// header
#include <semaphore.h>
class Foo {
    private:
        //declaration
        sem_t firstDone;
        sem_t secondDone;
    
    public:
        Foo() {
            // initialize
            sem_init(&firstDone, 0, 0);
            sem_init(&secondDone, 0, 0);
        }

        void first(function<void()> printFirst) {
            printFirst();
            //broadcast signl: first has done
            sem_post(&firstDone);
        }

        void second(function<void()> printSecond) {
            // waiting the signal from firstDone
            sem_wait(&firstDone);
            printSecond();
            //broadcast signl: second has done
            sem_post(&secondDone);
        }

    void third(function<void()> printThird) {
            // waiting the signal from secondDone
            sem_wait(&secondDone);
            printThird();
    }
};

Ref.
https://www.guru99.com/mutex-vs-semaphore.html
https://sls.weco.net/node/21326
https://jasonblog.github.io/note/linux_system/mutex_yu_semaphore_zui_da_de_cha_yi_shi.html