Both are the same thoughts. But the essence is Making a commitment is like a promise of doing something while giving is like sharing whole heartedly.

Hi! Both have the same meaning which is to make a promise and be willing to do what you promised! I hope I've helped you!

We normally say make a commitment, but everyone will understand you if you say give a commitment. I think to make a commitment sounds more empowered and like you are taking charge in English and to give sounds more passive like you are gently offering something.

I am a native gringo, I always say "make a commitment." I never use "give a commitment." Pero esto puede ser diferente en otros lugares que hablan inglés.

Both are the same and mean exactly what you said, promising something. However saying "to commit to something" means that you give something your full undivided attention