The verb “commit” has numerous related noun forms: commitment, commission, committal and committee. Many people – native English speakers included – do not know all the differences between them.
A criminal “commits a crime”. But we cannot talk about the “commitment of a crime”. Instead we say “commission of a crime”.
We use the word “commitment” to describe something that you have to do or something that requires time and responsibility – i.e. something you have promised to do or have to do due to, e.g., work or family reasons. We can talk about “family commitments” or “work commitments”.
When we promise to do something or take on a responsibility, we “make a commitment”.
For example: I’d like a dog, but it would be such a commitment, and I simply don’t have the time.
This usage of the noun is countable.
If you “show commitment” you demonstrate that you are willing to do something.
For example, an employer might include the following in a reference about a former employee: David is a very diligent worker and showed enormous commitment to the job.
This usage of the noun is uncountable.
The word “commission” can be a noun and a verb.
We can talk about the “commission of an offence/murder” as well as a crime.
A “commission” can be a request to do a piece of work or carry out an activity: We’ve got a commission to investigate allegations of corruption.
As a verb, “commission” has the same meaning: I’ve been commissioned to write a series of articles on alternative energy sources.
A “commission” can be a fee for an agent to carry out certain work: As a sales rep I don’t earn a salary, I get a 20% commission on each sale.
A “commission” can also be a group of people appointed and given the power (i.e. commissioned) to perform certain tasks.
A “committee” is also a group of people, but differs from a commission in that its members are representatives of a parent body. A committee makes decisions on behalf of the parent body.
A “committal” is an act of entrusting something or someone to the care of another person. So, for example, you can have a committal of property to an attorney, or a committal of a person to a mental health institution. In the latter case we talk about someone being committed to an institution.